The incident occurred in a village to the north of the capital, Makhachkala, late on Thursday.
"The businessman left the billiard room after a brawl with several other patrons and returned with a Kalashnikov assault rifle starting firing indiscriminately," a police official said, adding the attacker was intoxicated at the time of the attack.
"Both of the injured were hospitalized. The police officer has been operated on. His condition is serious but stable," the official said.
Police are searching for the businessman, involved in the automobile trade, who fled the scene.