Sheffield United:Police involved in Ched Evans issue causes olympic star to speak out
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."