Brown, 19, responded to Evans' five-year prison sentence by tweeting his support for Evans.
A statement released on the club's official website read: "Sheffield United confirmed today that an internal investigation is under way into social media comments made by reserve-team player Connor Brown following the verdict in the Ched Evans trial."
The statement continued: "The club is aware of a very serious matter regarding comments made through the Twitter account of one of its players. As a result we have launched an inquiry."
A complaint about the comments was made to North Wales Police by a leading rape charity.
Evans was jailed at Caernarfon Crown Court on Friday after being found guilty of raping the woman who was "too drunk to consent".
A spokeswoman for North Wales Police said: "We are aware of some comments made on social media sites and we are collating all relevant information."
Evans admitted having sex with the victim, then aged 19, at a hotel in north Wales last May.
In her evidence, the woman said she has no memory of the incident and the prosecution argued she was too drunk to consent to sexual intercourse.
Evans' co-accused, Port Vale defender Clayton McDonald, 23, who also admitted having sex with the victim, was found not guilty of the same charge.
Source: PA
Source: PA