It is the latest in a long list of misdemeanours involving Bellamy.
Last November, the 27-year-old Wales striker was cleared of assaulting two women in a Cardiff nightclub, while he was forced out of former club Newcastle United two years ago by then manager Graeme Souness following a series of disputes.
He has struggled to find his best form since arriving at Anfield in a £6million move from Blackburn Rovers last summer, scoring eight times in 31 appearances.
Nevertheless, Bellamy is expected to be in the squad that travels to Barcelona tomorrow morning ahead of the first leg of their Champions League first knockout round tie at the Nou Camp on Wednesday.