Ozil, who has recently been linked with a move to Barcelona, travelled to Lancashire ahead of Sunday's dramatic 1-0 win but was ruled out of contention on matchday and returned to London.
Arsenal clearly missed the Germany international as they battled to break down Sean Dyche's side until a stoppage time penalty from Alexis Sanchez settled the contest.
And the Gunners will likely have to make do without Ozil's services at Emirates Stadium on Wednesday.
"I don't know [what the illness is], I haven't seen him," Wenger said at his post-match press conference.
"The doctor came to see me and said he had to travel back home. He was in the hotel with us.
"Certainly he will be short for Wednesday. We will see what it is exactly."
Arsenal's win at Turf Moor - their third successive 1-0 victory away to Burnley - meant they leapfrogged rivals Tottenham into fourth on the Premier League table.