Aguero limped off just before half-time of the 5-0 win at the Etihad Stadium and manager Pep Guardiola admitted afterwards the injury "does not look good".
After undergoing assessment on Tuesday morning, the Argentinian will now travel to Barcelona to be examined by Dr Ramon Cugat, who has treated a number of City players in the past, ahead of possible surgery to correct the problem.
A statement released on Tuesday read: "Sergio Aguero suffered damage to his left knee in our recent 5-0 win over Burnley.
The scans I did this morning have confirmed that I have damaged my left knee. It's a pity but I'm in good spirits and so focused to come back as soon as possible. Thank you very much for all your messages!— Sergio Kun Aguero (@aguerosergiokun) June 23, 2020
"The striker will now travel to Barcelona to see Dr Ramon Cugat for further examination. Everyone at City wishes Sergio the best with his recovery."
Aguero confirmed that diagnosis on social media shortly after.
"The scans I did this morning have confirmed that I have damaged my left knee. It's a pity but I'm in good spirits and so focused to come back as soon as possible. Thank you very much for all your messages!" Aguero wrote.
Guardiola suggested on Monday night that Aguero, who has scored 23 goals in all competitions this season, could be forced to sit out the rest of the campaign.
"It doesn't look good," he said immediately after the final whistle.
"We will see. 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."