The left-back is suffering with a calf issue and he missed Saturday’s FA Cup defeat to Southampton.
Tierney was also forced to be absent on Tuesday, as Arsenal retuned to St. Mary’s in the Premier League to beat Saints 3-1.
Arsenal are next in action against Manchester United on Saturday, but Arteta is unsure if Tierney will be fit in time.
“I don't know. He wasn’t available against Southampton in the FA Cup. He was injured,” said Arteta.
“He is still injured today. And let’s see how he progresses for the game against Man United.”
Arsenal’s injury problems were also added to during Tuesday’s win over Southampton as Emile Smith Rowe and Thomas Partey had to come off.
Asked if Partey just came off with cramp, Arteta said: “We don’t know. He was feeling some discomfort. Hopefully it is nothing, but he was struggling.”
And on Smith Rowe, Arteta added: “He was injured for the game in the FA Cup, so he wasn’t available.
“We knew that today he could probably not play the whole game and he has some muscular discomfort. He had to come off again.”