The 21-year-old was punished after he was found in a nightclub with teammates until the early hours of the morning last weekend and his future at the Turkish club has now been called into question.
Besiktas coach Tayfur Havutcu said: "This is not the place to vacation. Besiktas have rules and discipline which the players have to obey. It is not allowed, except in reasonable hours, to be inside nightclubs.
"At this stage, it is not possible to say how long the penalty will last. It could be one week and then forgotten or the players could stay out of the squad until the end of the season."
Manchester United signed Bebe from Portuguese Guimaraes for £7.5m in the summer of 2010.