The Interior Ministry said another seven troops were injured in the incident, which took place today during a reconnaissance operation near the village of Yandi, some 40 kilometers (25 miles) outside the Chechen capital, Grozny.
Police gave no indication of who they believe set the bomb. An investigation is ongoing.
Chechnya was devastated by separatist conflicts in the mid-1990s and early 2000s, but has since attained a degree of stability under Kremlin-backed local strongman Ramzan Kadyrov.