Police personnel raided the house of Parida, a retired colonel, in Nayapalli area of the city Friday night after some relatives went to meet the couple but did not find the woman.
Suspecting foul play they informed the police.
During a search, police stumbled upon an iron box in which the chopped body parts were found. Some dissecting instruments were also there.
Police believe 71-year-old Somanath Parida killed his wife Usashri about a fortnight ago and had chopped her body in to small pieces. He was also allegedly quietly disposing them off over the past few days.
Parida was arrested on the basis of evidence against him, assistant commissioner of police BC Mishra said.
Police are yet to ascertain the exact reason behind the murder.
Parida's son and daughter live abroad.