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.