A lawyer for Breonna Taylor's family has called the grand jury proceedings a "sham" that has shown racial inequalities in the US justice system.
Ms Taylor, a black hospital worker, was shot six times and killed aged 26 when police raided her home on 13 March.
On Wednesday, a grand jury in Kentucky returned a minor felony charge against one of three officers, for shots that hit a neighbouring apartment.
Two officers have been shot amid protests sparked by the decision.
The individual indicted in the Taylor case is Brett Hankison, who was fired from the force in June. He faces three counts of "wanton endangerment in the first degree".
Under Kentucky law, wanton endangerment applies to an act of "extreme indifference to the value of human life". It is the lowest-level felony and carries a maximum sentence of five years in prison per count.
Ms Taylor's family had called for the arrest of all three officers, but the grand jury - a panel drawn from members of the public to determine whether there is enough evidence to pursue a prosecution - has declined to do so.
Attorney Ben Crump said in a tweet: "The grand jury proceedings were a SHAM. The 'wanton endangerment' charge is an example of America's 2 justice systems - protecting white neighbours & ignoring the death of a black woman."
"We've been saying 'Say Her Name' for six months... and #BreonnaTaylor's name was NEVER mentioned in yesterday's indictment," he later added.
In an op-ed for the Washington Post titled "Our devilish, racist system made it impossible to get justice for Breonna Taylor", Mr Crump rejected the notion that "every time justice is denied to a Black person in the United States, it seems the devil is in the details".
Most police shootings go unnoticed by the public, he continued, adding: "We wouldn't know Breonna's name if her death hadn't happened in a season of police killings when America was getting quickly woke to it.
"But now that the world knows Bre's name, we won't stop saying it until it becomes a kind of incantation to bind the devil in our divided justice system."
The two other officers involved were justified in their actions, the Kentucky attorney general said on Wednesday.
One had been hit by a shot fired by Ms Taylor's boyfriend, who later told police he thought it was an ex-boyfriend of Ms Taylor who had broken into the apartment.
A judge had granted a warrant to search Ms Taylor's home because investigators suspected her ex-boyfriend, a convicted drug dealer, was using the address to receive packages. Ms Taylor had no criminal record.
Cases of killings of unarmed black people by police have fuelled anger across the US and beyond, spurred especially by the death of George Floyd in police custody in Minneapolis in May.
What is happening in Louisville?
Protests were sparked across the US by anger over the grand jury decision. In Louisville, a state of emergency has been declared and the National Guard has been deployed.
A curfew is also in effect from 21:00 to 06:30 (01:00-10:30 GMT). Police say at least 127 arrests were made in Louisville overnight. Most arrests were for breaking the curfew.
The two police shot during the unrest on Wednesday were identified as Major Aubrey Gregory and Officer Robinson Desroches. Major Gregory has already been released from hospital, officials say, and Mr Desroches is recovering.
Twenty-six-year-old Larynzo Johnson has been arrested as the suspected gunman.
According to the Associated Press, the attack happened as protesters were moving through an alleyway to avoid a police roadblock as officers threw pepper balls at them. As shots rang out, the crowd scattered to take cover as officers in riot gear and rifles swarmed the area.
Protests over the grand jury's decision also took place in New York, Washington, Atlanta, and Chicago.
What did officials say on Wednesday?
Following the decision, Kentucky Attorney General Daniel Cameron - the state's top prosecutor - said there was "nothing I can offer [Ms Taylor's family] today to take away the grief and heartache as a result of losing a child, a niece, a sister and a friend," calling it a "gut-wrenching emotional case".
Mr Cameron said a ballistics report had found that six bullets had struck Ms Taylor, but only one had been fatal. That analysis concluded that Detective Myles Cosgrove had fired the shot that killed Ms Taylor.
The attorney general said it was not clear if Mr Hankison's shots had also hit Ms Taylor, but they had hit a neighbouring apartment.
He said Mr Cosgrove and the third officer, Jonathan Mattingly, had been "justified to protect themselves and the justification bars us from pursuing criminal charges".
The FBI was still investigating potential violations of federal law in the case, Mr Cameron added.
What has been the reaction?
Ms Taylor's relatives and activists had been calling for the three officers, who are all white, to be charged with murder or manslaughter.
When asked about the charges at a White House news conference, US President Donald Trump said he "thought it was really brilliant".
He praised Kentucky's attorney general, who addressed the Republican party convention last month, for "doing a fantastic job".
Mr Trump's Democratic challenger for November's election, Joe Biden, said the decision "does not answer" the call for justice, while telling protesters to act peacefully.
Kentucky Governor Andy Beshear, a Democrat, urged prosecutors to release the evidence that was presented to the grand jury.
"I think having more of the facts out there so people can see, people can truly process it, is where we need to be," he said.
Congresswoman Nancy Pelosi, the most senior Democrat in Washington, said on Thursday that "justice was denied for Breonna Taylor and her family".
Senator Kamala Harris, who is running for vice-president with Joe Biden, wrote on Twitter that Americans must "keep speaking Breonna Taylor's name".
What were the circumstances of Ms Taylor's killing?
Plainclothes police, executing a search warrant, forced their way into the apartment where Breonna Taylor was in bed with her boyfriend, Kenneth Walker, shortly after midnight.
Mr Walker fired a shot from his licensed gun, later telling police he thought that Ms Taylor's ex-boyfriend, Jamarcus Glover, had broken in, according to the New York Times.
Officials say Mr Walker's bullet struck Mr Mattingly in the leg. The three officers returned fire, discharging 32 rounds, according to a ballistics report from the FBI.
Ms Taylor was shot amid the commotion and died on the hallway floor.
A timeline of the shooting
- Walker fires one bullet, hitting Mattingly in the leg moments after police take down the flat door with a battering ram
- Mattingly returns fire, shooting six times at Walker and Taylor, who is standing beside him in her hallway
- Cosgrove fires 16 shots from the doorway of Taylor's home
- Taylor is struck six times in a matter of seconds
- Hankinson fires 10 shots through a patio door and window. His bullets enter the nextdoor flat
No drugs were found at the property, though Jefferson County Prosecutor Thomas Wine said the search was cancelled after the shooting.
A subsequent police report contained errors, including listing Ms Taylor's injuries as "none" and saying no force was used to enter, when a battering ram had been used.
Mr Hankison was fired from the police after investigators found he had "wantonly and blindly fired 10 rounds" during the raid, according to his termination letter.
Mr Mattingly and Mr Cosgrove were reassigned to administrative duties.