Three females named Zala, Nima and Run Run and one male called Kiumbe were tested after displaying mild symptoms.
Two staff members also tested positive for the virus, the zoo said.
An investigation is under way to establish how the animals became infected, but it is thought they may have been in contact with an asymptomatic member of staff.
Zookeepers reportedly carried out a standard PCR swab test on the four lions - the same method used on humans - because they are comfortable having close contact with staff.
The animals had been showing upper respiratory symptoms, according to an earlier statement from the zoo. Most symptoms have disappeared other than minor coughing and sneezing.
They are being treated with anti-inflammatory drugs and monitored closely.
"The lions were given veterinary care for their mild clinical condition - similar to a very mild flu condition - and [they] responded well," a statement said.
The Veterinary Service of Barcelona contacted colleagues at the Bronx Zoo in New York, where four tigers and three lions tested positive for Covid-19 in April.
One of the tigers, Nadia, is believed to be the first known case of an animal becoming infected with Covid-19 in the US.
It is the only other zoo where large felines are known to have contracted coronavirus. All made a full recovery.
The four-year-old male and the females, who are all 16 years old, have had no contact with other animals at the zoo, which is open to visitors.
The risk of infection between zoo animals and visitors, meanwhile, is low became of a lack of proximity. "Simply, no one who comes to see [the lions] gets close enough," the Barcelona Zoo statement said.