United and Wales forward Evans, 23, was jailed for five years on Friday after being found guilty of raping a 19-year-old woman at a hotel in Rhyl, North Wales, in May last year.
Prosecutors said the victim was "too drunk to consent".
As well as tweeting his support for Evans, Brown called his victim "a money-grabbing little tramp" and launched what the Sheffield Star newspaper said was an "extraordinary swear-word filled rant" at the woman.
English third tier promotion hopefuls United said in in a statement issued Monday: "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 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."
Under English law, all alleged victims of rape are supposed to have their identity protected for life but the Star reported Monday that the "Internet has also apparently been used to illegally name the girl".
Evans, who has scored 35 goals for United this season and has 13 caps for Wales, had admitted having sex with the woman but told the court during the trial she had consented.
Source: AFP
Source: AFP