The bomb went off late on Monday near the village of Novy Tsentoroi when a Defense Ministry convoy was passing.
In a separate incident, an unidentified gunman in a car fired shots at police, before blowing up his vehicle in the Chechen capital, Grozny.
"The car was damaged and stopped when police returned fire, and the unidentified man, who was behind the wheel, detonated an explosive device and blew himself up," the source said.
The attacker died at the scene. His identity is being established.
Also on Monday, an unidentified man was killed in Chechnya's Zavodskoi district. The man, driving a Lada car, opened fire on private security guards with a Kalashikov assault rifle while crossing a checkpoint, and was killed when they returned fire.
Militant attacks have continued since the official lifting last month of the Kremlin's decade-long anti-terrorist campaign in the North Caucasus republic.
Violence often spills over into nearby republics, in particular Ingushetia and Daghestan.
Late on Monday, four Chechen police were killed in neighboring Ingushetia when a tripwire bomb went off during a joint Chechen-Ingush police operation.
