Kumar, the first policeman in the national capital to die due to coronavirus, was posted at the Bharat Nagar Police Station in northwest Delhi, they said.
After his condition deteriorated on Tuesday evening, he was taken to the Ram Manohar Lohia Hospital, where he was declared brought dead by doctors.
Kumar's sample was sent for COVID-19 test and the reports came as positive on Wednesday, police said.
Chief Minister Arvind Kejriwal condoled the demise of the constable and said his family would be provided with an ex-gratia of Rs 1 crore.
Joint Commissioner of Police (Northern Range) Manish Agrawal, Deputy Commissioner of Police (Northwest) Vijayanta Arya and other officers of the district paid their last respects to the deceased at Punjabi Bagh crematorium.
The joint commissioner of police interacted with the family members of Kumar and conveyed his condolences in this hour of grief. AMP SNESNESNE