The 23-year-old is expected to be sidelined for up to a month after limping off in the 2-2 draw with Liverpool and may miss the Champions League clash with Bayern Munich
The 23-year-old limped out of the Gunners' 2-2 draw with Liverpool before being replaced by Brazilian Andre Santos.
"Gibbs has a thigh strain and will be out for three weeks. It's a big blow for us," Wenger said in his post-match press conference.
"He was an important player for us going forward and the game we wanted to play. It's a shame he's out for the next three weeks."
Gibbs will certainly miss Saturday's Premier League game with Stoke City, but the young left-back may also miss out in the Champions League against German giants Bayern Munich.
Wenger admitted he may be forced into the transfer market to replace Gibbs, who spent some of last season on the treatment table with a hernia.