Ibaka was involved in a confrontation with Los Angeles Lakers forward Metta World Peace on Friday which led Jackson, a friend of Peace's, to issue a threat to Ibaka on the social networking website.
The San Antonio Spurs said they supported the punishment.
"The recent public comments made by Stephen Jackson are absolutely unacceptable, cannot be tolerated and do not reflect the standards held by the San Antonio Spurs," General Manager RC Buford told the team's website.
Jackson has a history of coming to the aid of Peace, most famously in the 2004-05 season when the then Indiana team mates were involved in a brawl with fans in Detroit.
Jackson received a 30-game suspension for that incident while Peace, then known as Ron Artest, was banned for the rest of the season. (Writing by Jahmal Corner in Los Angeles. Editing by Patrick Johnston)