The France international sustained the problem in Sunday's 3-0 defeat to Manchester City at St Mary's Stadium and was forced off at half-time.
Koeman confirmed on Monday that Schneiderlin will miss Wednesday's trip to Arsenal with a scan yet to confirm the full extent of the midfielder's absence.
The Dutchman also acknowledged what a blow it is to lose the 25-year-old, who has been a vital figure in Southampton's strong early-season form.
"He's not ready for Wednesday. He's now having a scan on his right leg, we have to wait and see the results of the scan," Koeman explained.
"His injury is up in his adductor. It's not too soon to say he can't play Wednesday but for how long we don't know.
"We know exactly what Morgan means for our team, he's one of our key players and without key players it's always difficult for the rest of the team.
"We can't do anything about that. We don't have the bench, the number of players, that big teams have."
