Ozil, 29, trained as normal in the days ahead of Sunday's (26 November) clash at Turf Moor but was the most notable omission from the Gunners starting XI with the club confirming his absence due to illness ahead of kick-off.
Alex Iwobi came into replace the former Real Madrid star with an injury time penalty from Alexis Sanchez sealing a narrow win for the Gunners.
Arsenal return to action on Wednesday when they welcome Huddersfield at the Emirates before hosting Manchester United on Saturday evening.
Speaking in his post-match press conference, Wenger explained Ozil returned to London ahead of kick-off and admitted he is likely to be a doubt for the visit of David Wagner's side.
"I haven't even seen him," Wenger said, the Evening Standard report. "The doctor came to see me and said he had to travel back home, he was in the hotel with us.
"He travelled up with us, then travelled back. We brought Maitland-Niles up who arrived at 1pm because we had only 17 players.
"Will he be available for Wednesday? Certainly he will be short. We will see what it is exactly."
Jack Wilshere was introduced as a second-half substitute after 67 minutes in the narrow win over Burnley, producing a bright performance off the bench as his side chased a winner. The England international is still waiting for his first Premier League start this season but Wenger hinted that opportunity could come soon.
He did alright when he came on, he has that little burst to be dangerous," Wenger said of Wilshere. "We play so many games and he is getting stronger."