A planted land mine went off on Friday night on a highway in the Nozhai-Yurt district, about 60 km (40 miles) southeast of the republic's capital of Grozny, when a column of police trucks was passing by.
"A driver of one of the trucks was killed in the blast," the source said.
Two weeks ago the Kremlin announced that its 10-year counter-terrorism operation in the troubled region had formally ended.
Russian federal troops launched the counter-terrorism operation in Chechnya in the fall of 1999 after a group of militants led by Shamil Basayev and Arab mercenary Khattab invaded neighboring Daghestan. Moscow conducted a separate campaign in Chechnya in 1994-1996.
Under President Ramzan Kadyrov, the republic has seen a decline in militant activity, although attacks on federal forces remain common. The 32-year-old Chechen leader has been accused by his critics of involvement in human rights abuses, a charge that he denies.
