The attack occurred at about 13.00 Moscow time (11.00 GMT) near the republic's largest city, Nazran.
"As a result of the attack one policeman died and another was taken to the hospital with serious wounds," the source said.
An investigation has been launched. Police are searching for a Russian-made Zhiguli sedan, which the assailants have reportedly used to flee the scene after the attack.
During the first five months of 2008 Ingushetia saw a sharp increase in assaults on law enforcement and military personnel. In 53 attacks a total of 12 police officers and four servicemen were killed and 46 law enforcement officers and 11 soldiers were injured.
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The main event of the third day of the 11th meeting of the Valdai International Discussion Club in Sochi was the closing session with President Vladimir Putin. The atmosphere was calm and open, despite the current political tensions and the Russia-West confrontation. The Russian president said that it corresponded to the spirit of the Valdai Club.