Separately, the Indian Navy quarantined around 150 officers and sailors at the INS Netaji Subhash, an administrative and logistics base in Kolkata, as a precautionary measure after its two sailors reported symptoms for COVID-19, official sources said.
All the 24 people who tested positive for the infection in the Research and Referral hospital were from its oncology ward. They have already been shifted to the Army's Base hospital in Delhi Cantonmen, they said.
The Base hospital has been designated to treat coronavirus patients.
The 24 people included 20 serving personnel from the three services, their dependents and a veteran, the officials said.
After a patient tested positive, authorities at the premier hospital carried out detailed contact tracing.
"Quarantine protocol and testing of those in the high risk group was carried out," said one of the officials.
It is the second biggest case of the coronavirus outbreak hitting the armed forces.
Last month, 26 Indian Navy personnel tested positive for the infection at the strategically-located Western Naval Command in Mumbai.
On Friday, Army Chief Gen MM Naravane said that 14 coronavirus cases were found in the Army and five of them have recovered so far.
The Indian Air Force has not reported any coronavirus case yet.
As of now, around 80 serving personnel were undergoing treatment for coronavirus across the country. MPB RDMRDM