The 27-year-old defender was forced off just before half-time during Saturday's goalless draw with the Premier League champions after dropping to the floor and clutching his right leg.
It is hoped the injury is a muscle problem, likely hamstring, but Stephens has struggled with a reoccurring knee issue recently, giving his manager Ralph Hasenhuttl some cause for concern.
"I don't know what it is but he has had knee problems. Hopefully it is not too bad," said Hasenhuttl.
"He was in perfect shape, he was a really important player for us. So early in the season an injury would not be good for us."
Hasenhuttl is likely to provide a fresh update on Stephens on Tuesday night, following Southampton's Carabao Cup tie against Sheffield United at Bramall Lane.
Meanwhile, Valentino Livramento continues to catch the eye, after another impressive performance at the Etihad Stadium.
The 18-year-old full-back, signed from Chelsea last month, has played his way straight into the team and started all five of Saints' Premier League matches this season.
"Yes, I must say I'm super happy with this guy," said Hasenhuttl. "He was run out of energy in the end so we took him off.
"He shows every week how strong he is and when you play against such players like these you have to be good and one against one he is.
"He never stays, he is always going and that's what I want from him. Physically he is a good guy, a good height for a full-back, a fantastic player. But keep it calm - don't talk too much about him!
"I tell him that he will play immediately when he comes to us and I think that was something that helped him decide on coming to us.
"Kyle Walker-Peters was in his position but Kyle is now on the left. That tells you everything because Kyle was very important last season."