The soldier, from a locally recruited special forces battalion of the interior ministry, was shot dead and another one wounded when their unit came under attack on Saturday, the state-run news agency RIA Novosti reported on Sunday, quoting a security source.
The incident took place in a forest near the village of Niki Khita in the south-eastern Kurchaloi district.
In a separate incident, two other soldiers were wounded after coming under fire in a forest near the village of Bugaroi, in the southern Itum Kale district, high in the mountains of southern Chechnya, the same source said.
There was no independent confirmation of the report.
Official information about fighting in Chechnya is rarely given out and independent reporting highly restricted.
Russian troops stormed Chechnya in 1999 after being defeated in a 1994-1996 separatist war.