The incident took place Wednesday at Guhalipal village, about 110 km from Bhubaneswar but came to light after police arrested the man a day later.
The trouble started Monday morning when accused Mahalia Nayak asked his wife Jhana, one year younger to him, to serve him tea. Enraged by the delay, he had a heated argument with her, investigating officer Dasarathi Nath told IANS.
The trouble intensified when the man continued to argue with his wife after she refused to cook and serve him food, he said.
Nayak raised the issue Wednesday night and killed her with a sharp weapon, Nath said.
Police have arrested Nayak after he confessed to the crime, he said.