Temporary alternatives are currently being considered for the venue, which was renamed in 2007 after a naming rights deal between 02 and the venue’s owner AEG.
The move is a result of IOC’s “clean venues” policy which aims to protect the rights of official partners.
The policy aims to safeguard the image of the Games by limiting the number of advertisements and branding inside Olympic venues.
British Telecom, the Games’ official telecoms partner, is understood to have paid about £80m for its tier one status.
The O2 Arena will play host to gymnastics and basketball during the games
Separately, Ansco Arena, the AEG subsidiary that runs the arena says pre-tax profit was £15.6m in 2008 against revenues of £53m in its first full-year of trading.
The O2 opened in June 2007 and registered sales of £27m in its first six months but reported a net loss of £9.7m in 2007 because of opening expenses.