Police are investigating after a Twitter user wrote that he hoped Ched Evans raped Jessica Ennis-Hill.
On Thursday the athlete said she would want her name removed from a stand named after her by Sheffield United if the club re-signs the convicted rapist.
Later in the day a tweet was sent, saying: "I hope he [Evans] rapes her".
The out-of-contract striker, 25, was freed last month after serving half a five-year prison sentence and has since been allowed to train with the club.
In a statement released on Thursday, 28-year-old Ennis-Hill, who is from Sheffield, said: "Those in positions of influence should respect the role they play in young people's lives and set a good example.
"If Evans was to be re-signed by the club it would completely contradict these beliefs," added the London 2012 Olympic heptathlon champion.
Within hours of her intervention the tweet was sent from an account that has since been deleted.
Prime Minister David Cameron told reporters on the eve of the G20 summit in Australia that he understood Ennis-Hill's decision.
Speaking at an off-camera briefing he said: "I quite understand why she's said what she's said and done what's she done."
'Taking a stand'
South Yorkshire Police said in a statement officers were "investigating reports of abusive tweets".
The statement said: "Officers are making efforts to contact the individual concerned, but have launched an investigation into the posts online."
Reacting to the controversy, shadow home secretary Yvette Cooper said Ennis-Hill had been "absolutely right" to speak out and it was "appalling she had now received rape threats".
Ms Cooper said: "Whether it's on Twitter or in the pub, wherever it is, it should still be a criminal offence and that's why the police need to investigate.
"And for it to happen when Jessica Ennis Hill has done exactly the right thing by taking a stand against violence against women, to be honest it shows why what she's done is so important."
Sheffield United manager Nigel Clough has said the club is "nowhere near decided" whether or not to re-sign Evans.
Evans has scored 59 goals in 167 appearances during spells with Manchester City, Norwich City and Sheffield United.
He was sentenced to five years in April 2012 for raping a 19-year-old woman in a hotel room in May 2011, having been found guilty by a jury at Caernarfon Crown Court.
At his trial, he admitted having sex with the teenager but denied rape.
He has declined any request to be interviewed by the BBC, but released a video statement on his personal website in which he said he wanted to play again.