Groves said in a statement Wednesday that he let a lot of people down, starting with his family, and he told fans, the Browns and the city of Cleveland he was sorry for putting himself in this situation.
"I am committed to learning from this and moving forward," he said.
Groves entered a no contest plea to disorderly conduct in Bedford Municipal Court in suburban Cleveland on Tuesday following his citation by police in neighboring Orange last Wednesday.
Court records show Groves also paid $365 as part of the case. The Browns declined to comment.
Police say Groves was taken into custody at a hotel after arranging in a phone call for sex acts with an undercover officer.
Groves signed a two-year, $2.8 million deal with the Browns last month as an unrestricted free agent. He had a career-high four sacks and made seven starts for the Cardinals last season.
Information from The Associated Press was used in this report.