54-year-old DS Murti was killed in the incident that was reported from the Mandir Marg area in Delhi, they said.
Mr Murti, who was a finance manager with a realtor, died at RML Hospital.
His wife KV Rama and her accomplice Shyam Singh alias Bhagatji have been arrested, DCP Madhur Verma said.
Mr Singh, a tantrik, had allegedly provided the poison, the officer said.
Ms Rama told police she was not happy in her marriage because of her husband's drinking habit. It also led to debt of Rs 10 to 12 lakh on the family, the DCP said.
Mr Murti's brother Siva Sarma had lodged a complaint in this regard, he said.