Aguero was substituted at half time during City's 1-1 draw with West Ham at the London Stadium on Saturday, having only recently returned from knee surgery which had kept him out of action since June.
The 32-year-old could now miss the bulk of City's Champions League group stage campaign, having not travelled with the squad for Tuesday night's clash with Olympique Marseille at the Stade Velodrome.
Aguero could also sit out of the Premier League meeting with champions Liverpool on a week on Sunday, butt Guardiola could not give a firm timescale on the striker's return.
"It depends on the injury," the City manager said at his pre-match press conference in Marseille. "10-15 days is the minimum. If it’s a little bit longer it will be three weeks, one month.
"The muscular [injuries] normally doesn’t move in these gaps and the case of Sergio will be the same, there will be no exception."
Guardiola insisted that City had not rushed Aguero back following the knee surgery which prevented him from making an appearance until the 1-0 win over Arsenal on 17 October.
“We didn’t rush back, we were incredibly patient, we didn’t force him, we didn’t force the doctors.
"When people tell me he’s ready, of course we knew he was not in the best condition to play and without training, but it was important to play 55-60 minutes.
“We tried to avoid the last 25-30 minutes, when muscles get tired, but unfortunately one action in the first half, he was unlucky. He went to stop a long pass and he felt something. Hopefully he recovers as well as possible.”