Aguero limped off just before half-time with a knee injury and will have a scan on Tuesday to determine the extent of the problem but Guardiola expects the striker to miss the trip to Chelsea on Thursday.
"It doesn't look good," said Guardiola. "We will see [on Tuesday]. He has struggled the last month with a problem in the knee and now he felt something but we will see exactly what he has. It doesn't look good.
"The doctor says it will take time. A few games [out] for sure but maybe the tests he will get good news we will see."
Aside from Aguero's injury, City enjoyed a comfortable night against Burnley, thanks, in part, to the performance of Phil Foden. Starting for just the fourth time in the Premier League this season, the 20-year-old midfielder scored two and helped create another for David Silva.
"When Phil plays, he's never played badly," said Guardiola. "Especially his behaviour and his attitude, it doesn't matter if he plays or doesn't play, he loves to play football.
"He loves being the first out for a training session with the ball, he loves to play and ever time he has played since he was promoted to play with us, he has always been a high level.
"But we cannot forget he is 20 and he has to improve. He will be an important player for our next decade at this club. The minutes he has, he deserves it."
After the game -- marred by a "White Lives Banner flown over the Etihad Stadium at kick-off -- Burnley manager Sean Dyche was critical of board decisions which left him with a threadbare squad to face City. On top of a host of injury problems, Jeff Hendrick, Phil Bardsley and Aaron Lennon were left out of the squad after choosing not to sign short extensions to their deals, which are all due to end on June 30.
"The club decided to offer month contracts late in the day and the players had to make a choice and their choice is not to be involved," said Dyche. "We are in incredible financial shape so there is a balance. We have been run very well financially in the time I have been here. I can only advise which I have done and the chairman decided to make different decisions.
"There is no lack of work [from the players picked]. They were disappointed with some of the things that happened to their teammates. City looked like they got their eye in and certainly delivered it."