The 21-year-old sustained a knee injury during the 4-0 Carling Cup win at Newcastle on Wednesday night.
Gibbs will undergo a scan on Friday.
“We lost Kieran Gibbs last night,” Gunners boss Arsene Wenger told Arsenal TV Online. “That is the bad news.
“It is a medial knee ligament strain. It needs to be checked on the scan tomorrow but it will be a few weeks.”