Gallas has struggled with the role at times this term.
And asked if he would remain as skipper, Wenger said: "I can't answer that question. I want to analyse the season, after the season has finished.
"At the moment, he will be my captain until the end of the season.
"I believe William has learned a lot this year. I can only say his commitment and desire to do well was exceptional.
"I don't want to go into any other individual assessment."
Centre-half Gallas, 30, lost the plot at Birmingham after the Gunners' shock 2-2 draw and Eduardo's horror leg-break.
The Frenchman refused to leave the pitch at the final whistle and sat alone in the centre circle, close to tears.
He walked off only after being called back by Wenger.
The gaffer added: "I made the decision to make him captain and I have to stand up for that decision."