Evans was jailed for five years for the crime at Caernarfon Crown Court last week after being found guilty of raping a 19-year-old woman in a hotel room near Rhyl, North Wales, in the early hours of May 30 last year.
Co-defendant Clayton McDonald, who plays for Port Vale, was found not guilty of the same charge.
In the wake of the verdict, reserve team player Connor Brown took to the social networking site to stick up for his team-mate and criticise the victim.
One of the three tweets he posted, which have since been deleted, read: "Money grabbing little tramp."
A club spokesman confirmed in a statement: "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."
Evans was named in the PFA's League One Team of the Year on Sunday after a vote which was closed last month, before his trial.
Police are investigating claims that the victim was named on Twitter and has received abuse via the site.
Holly Dustin, director of the End Violence Against Women coalition, as well as Rape Crisis England and Wales, said: "It is profoundly disturbing that the victim in the Ched Evans trial has been named and abused on Twitter and other social media sites.
"It has long been law that rape complainants are protected by lifetime anonymity and those who have named her have been reported to the police for committing a criminal offence."