Sagna is expected to be out for one match with Carl Jenkinson set to replace the French full-back as the Gunners seek to increase their lead at the top of the table.
"I believe we will lose Sagna who has a slight hamstring problem and he should be out for tomorrow's game," manager Arsene Wenger said.
"You expect when you play so many games with that much intensity that you will lose one or two players.
"We have so many games that I always knew I'd have to make changes. Full-back is a demanding position."
Lukas Podolski is expected to return to training this week having recovered from his own hamstring injury with the trip to Manchester City on December 14 the earliest possible date for the German forward's return.
"Lukas Podolski should be back in normal training after the Hull game," Wenger said.
"He will then be available but he lacks is match fitness. It will take at least a week with normal training to consider him fit for the squad."
Wenger denied reports that he has agreed a six-month loan deal for Real Madrid striker Alvaro Morata and that a £6million bid for Brazilian marksman Alexandre Pato has been rejected by Corinthians.