Ramsey played the full 90 as Arsenal snatched a late draw against the Saints.
But the Welshman hobbled through the last few minutes and after the match Wenger confirmed the midfielder had an injury.
Ramsey is now a major doubt for Wednesday’s clash with West Ham and a busy period of fixtures.
And it means Jack Wilshere could get a run in the team after failing to start a league game this season.
Wenger said: “Aaron Ramsey couldn’t play at the end. He had a hamstring problem.”
He added: “It was a difficult game and I felt that we paid a heavy price for a slow start. We kept going. It was a game of high intensity.
“In the second half it was all us but they defended well. We played with many strikers.
“Overall, I think the spirit was great. We were relentless to the end.
“I consider Olivier Giroud as a regular player. We have to be grateful that he is part of a great team and one who can come on and make a difference with the right attitude and ability. He is a talent.”