The incident was captured on the security cameras of the store in the Colombian capital city of Bogota.
Fray Vicente Ardila Velázquez is seen throwing other women around the store to which he followed his wife because they had fallen out earlier in the day.
The police officer, whose name has not been officially released, then ran from the store leaving his wife, Angie Katerine Herrera, for dead.
But he was grabbed by eyewitnesses and passersby who held him until police officers arrived to arrest him.
The policeman had followed his wife to the supermarket in the Tunjuelito area of the city after they argued at home earlier that day.
Friends and neighbours said the couple had not been getting on well for some weeks.
The police officer, who was on leave, is being held in police custody and faces murder charges.
Bogota was considered one of the most violent cities in the world in the 1990s but is much improved following a ban on carrying guns in public.