Armenia international Mkhitaryan, who arrived at the Emirates in January from Manchester United in a swap deal involving Alexis Sanchez, was forced off just after the hour mark in Thursday's 4-1 Europa League quarter-final, first-leg victory over CSKA Moscow.
The 29-year-old, who has scored one Premier League goal for the Gunners, was seen clutching his knee and, after the match, Wenger confirmed the midfielder will not be fit enough for the clash against the Saints.
He said: "He has a knee problem, we don't know how bad it is, we have to assess it tomorrow morning. He will certainly be out for Sunday."
Wenger has also revealed number two keeper David Ospina, who was replaced in goal by Petr Cech for the European encounter, will be out of action for the next two-to-three weeks with an ankle injury.
"The scan today was reassuring, he will be out for two to three weeks," he added.
"Yesterday we were scared it was a very serious injury but the scan was reassuring. Yes [he did it in training] - he just moved back from a shot and sprained his ankle, without any contact. It was just a bad movement."
Arsenal's only major absentee is midfielder Santi Cazorla who is not expected to return until next season.