Letters encouraging recipients to take part in "Punish a Muslim Day" have reportedly been sent to addresses across the country.
Images of the A4 notes, which contain a list of violent acts alongside a number of points for performing them, have been widely shared online.
They have prompted a chorus of condemnation, with campaigners and MPs describing them as "disturbing".
Counter-terrorism police are treating the letters as a possible hate crime.
'Fear in the community'
Tell Mama UK, which monitors anti-Muslim activity, said it had received reports of people in Bradford, Leicester, London, Cardiff and Sheffield getting the letters.
Director Iman Atta said: "This has caused quite a lot of fear within the community.
"They are asking if they are safe, if their children are safe to play outdoors.
"We have told them to keep calm and to phone the police if they receive one of these letters."
She said a number of the letters had been posted from Sheffield and bore a similarity to letters sent to mosques in the UK and US in May 2017, which were also posted from Sheffield.
"They are inciting violence against the Muslim community," she said.
Labour MP Naz Shah said several of her constituents in Bradford had received the "hate mail" through their doors.
Ms Shah said the letters were an attempt to instil fear but one that would ultimately fail.
"We stand shoulder by shoulder, and stand side by side, because nothing will divide us," she said.
"This is hatred and it just doesn't work. You know, it's what we do."
She said she had spoken to police, and had been told detectives believed they were dealing with a "linked series of offences".
Counter Terrorism Policing North East said it had received reports of "potentially malicious communications sent to individuals across the UK".
A police spokesperson said: "Counter Terrorism Policing North East are co-ordinating the investigation at this time and will consider any potential links to existing inquiries.
"Anyone with any concerns about a communication they may have received should contact their local police force."
West Yorkshire Police said it had received six reports while South Yorkshire Police said it had received three.
A Metropolitan Police spokesman said it had received two reports of letters being sent to people, one in east London and the other in the SW4 area.