The deaths were reported Friday in the suburb of Zheleznodorozhny.
An officer died and a second was severely injured after the driver of a vehicle they pulled over threw an explosive device at them, said Olga Vrady, a spokeswoman for Moscow's investigative committee.
Police were searching for the suspect.
Earlier, another police officer was allegedly beaten to death by a person involved in a car accident in Zheleznodorozhny, police said.
As the officer filled out paperwork for an accident between a Lada-2104 and a BMW, the driver of the Lada allegedly attacked and beat him, the Moscow region's Interior Ministry said.
Police arrested the driver and tested him for drug and alcohol intoxication, RIA Novosti reported.