The burning body parts were found on Friday night and Saturday morning in Goldbeck near Buxtehude, less than two miles from the couple's home. The man denies the charges. Police spent Sunday searching the home and the man's car.
A police spokesman said investigators believe the murder is the culmination of a domestic drama that has been continuing for several years, but refused to add any details.
The couple lived alone and had one grown-up daughter.
The body parts were discovered by motorists who noticed the fires at the side of the road on Friday night. Pedestrians found the woman's head, also burnt, and several items of clothing on Saturday morning.
A search was carried out involving around 100 firefighters, and several more plastic bags containing unburnt body parts were discovered in the area.
The identity of the murder victim was confirmed on Saturday night by police doctors. Relatives had reported the woman missing on Saturday evening.
Her husband was arrested soon after.