Nine soldiers were also wounded in the attack early on Monday.
Six soldiers were killed and five wounded in 18 attacks on Russian positions by Chechen separatists over a 24-hour period, an official said on condition of anonymity.
In a separate incident, three soldiers were killed and three were wounded when their armoured vehicle ran over a mine in Chechnya's southern Vedeno region.
Also in southern Chechnya, one soldier was killed and another was wounded in clashes with Chechen separatist fighters that also left one fighter dead.
Meanwhile, in the Chechen capital Grozny, one police officer was shot dead at a street market. The assailant ran away, but some 20 people were arrested.
Russian troops entered Chechnya in October 1999 to try to re-establish control following defeat in a first war against separatists in 1994-96.
Although major clashes have become rare, Russian forces and local Chechen allies continue to suffer almost daily casualties.