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.
