Tino was diagnosed with the virus after displaying symptoms including shortness of breath, sneezing, and a runny nose on 9 July. The nine-year-old big cat also lost his appetite.
Within two days, 12-year-old Hari was showing the same symptoms. Both are now said to be recovering from the disease.
In a statement on Sunday, Suzi Marsitawati from the Jakarta Parks and Forestry Agency confirmed swabs taken from the two animals showed positive results for Covid.
The tigers underwent treatment with antibiotics, antihistamines, anti-inflammatory drugs and multivitamins.
After 10-12 days and under close observation at Jakarta's Ragunan Zoo, the pair’s condition was said to be improving and both animals have now recovered.
“Their condition is good now. Their appetite has returned and they're being active,” Ms Marsitawati said.
An investigation has been launched into how they contracted the virus since the zoo has been closed to visitors as part of coronavirus restrictions.
Ms Marsitawati said there were no known infections among the caretakers and other zoo staff that could have led to the tigers contracting Covid.
Indonesia has become Asia's hot spot with a record number of coronavirus cases in the region.
Sumatran tigers are the most critically endangered tiger subspecies and are under increasing pressure as their jungle habitat shrinks.
There are estimated to be fewer than 400 alive today living in the remaining patches of forest on the island of Sumatra.
But deforestation and poaching means the species faces extinction; a fate which has already befallen its Javan and Balinese counterparts.
Additional reporting by AP
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