The Manchester City striker has missed four straight games after coming into contact with another person who had contracted COVID-19.
Aguero announced his result on Twitter and it is not known when he will be free to return to training.
"After a close contact, I've been self-isolating and the latest test I took was positive for COVID 19," Aguero wrote.
"I had some symptoms and I'm following doctor's orders for recovery. Take care, everyone."
Aguero has played in just five Premier League games and nine matches in all competitions in a stop-start campaign.