"Sanjay (husband of Kumari Selja's maid) was beaten to death by (cook) Anil Yadav in a scuffle on Monday," said a police official.
Yadav was detained as he had some injury marks on his face.
"Yadav's clothes, which he was wearing during the murder, were also recovered," the official added.
On Monday, the police recovered a body from Kumari Selja's house.
The body of Sanjay, who is the husband of a maid at Selja's residence, was spotted by a security guard around 8 a.m. inside the servant quarter of the minister's house in central Delhi's Sunehri Bagh area.