Walcott, 28, was replaced mid-way through the second-half on Wednesday (20 September) after scoring the only goal of the game as the Gunners sealed an unconvincing win over League One opposition.
The England international will undergo further tests today but his manager explained at a press conference on Thursday: "We don't think it is much."
Calum Chambers was also handed a rare start but was replaced by Josh da Silva at half-time. The former Southampton defender has joined Danny Welbeck on the sidelines with what Wenger described as a "little recurrence of a hip injury" that will rule him out until after the international break – with their league campaign resuming away to Watford on Saturday 14 October.
The Arsenal boss also confirmed that trip to Vicarage Road is Welbeck's likely return date.
"He [Welbeck] has groin injury but he will be back, his target is Watford, so after the international break. He won't be able for England or for us [until then]."
Ozil meanwhile had previously been ever-present in the Gunners starting 11 this season until a knee injury forced him out of last Sunday's goalless draw with Chelsea. But with a return to training imminent, he could be line for a return for the visit of Tony Pulis' side on Monday.
On the Germany international, Wenger said: "He is in training. He will come back into the team maybe tomorrow."
Jack Wilshere meanwhile started his first game for the club since the final day of the 2015-16 season with Wenger confident the midfielder came through the 90 minutes unscathed.
"That what we expected, I don't think there were any problems, he came off the pitch very well," Wenger added.
Wilshere is in the final year of his contract at the Emirates with his manager having already thrown down the gauntlet and challenged him to earn a new contract.
On whether his midfielder will get a new deal, Wenger said: "That is down to if he can remain fit or not. I think he is an Arsenal man and an Arsenal player. I don't know, we haven't spoken about that, we have to see how it evolves and what kind of influence he can have on the squad over the course of the season."