Constable Rahul, 30, had underlying health conditions and he breathed his last on Wednesday at Safdarjung Hospital, the police said.
He was on a medical leave since November 2019 and was undergoing treatment for lung infection. "Almost 85 per cent of his lungs were not functioning," Deputy Commissioner of Police (northeast) Ved Prakash Surya said.
Earlier, three Delhi Police personnel died due to COVID-19.
Rahul, a native of Aligarh in Uttar Pradesh, was posted in northeast district and resided with his family in Mandoli area here.
A senior police officer said the constable was being treated at a health facility in south Delhi and was shifted to Safdarjung Hospital on Tuesday after his condition deteriorated.
Around 500 personnel of the force have been infected with the dreaded virus and 200 of them recovered, according to Delhi Police.
A 31-year-old constable, Amit Kumar, posted at the Bharat Nagar police station had died on May 6, while two assistant sub inspectors succumbed to the disease last week.
Assistant sub inspectors Shesh Mani Pandey, 54, and Vikram, 52, died while undergoing treatment for the disease at the Army Base Hospital here in the last week of May.
Vikram was posted at the Sultanpuri police station of outer Delhi and was on highway patrol duty in the area since May 1.
Pandey was ex-Army personnel and worked with the Finger Print Bureau (FPB) of the Crime Branch in Central Delhi's Kamla Market area. NIT DPB