Brown, 19, responded to Evans' five-year prison sentence by tweeting various comments in relation to the case and his support for his team-mate.
A club statement read: "Sheffield United Football Club have suspended reserve team player Connor Brown with immediate effect pending an internal investigation into comments apparently posted on his personal Twitter account.
"There will be no further comment from the club during the process of the investigation which it hopes to conclude swiftly."
A complaint about Brown's comments on Twitter was made to North Wales Police by a leading rape charity.
Evans, 23, was jailed at Caernarfon Crown Court on Friday after being found guilty of raping the 19-year-old woman, who was "too drunk to consent", at a hotel in North Wales last May.
Port Vale defender Clayton McDonald, 23, who also admitted having sex with the victim, was found not guilty of the same charge.