A statement on the club's official website read: "Sheffield United confirmed today that an internal investigation is underway into social media comments made by reserve team player Connor Brown following the verdict in the Ched Evans trial.
A club spokesman said: "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 jailed for five years on Friday for a rape offence which took place in Rhyl, Wales, last year.
In their first game without him, the Blades fell to a 1:0 defeat at MK Dons in front of over 6,000 travelling fans, with Evans being a notable absence.