Byutukayev was one of six militants killed during a special operation in the village of Katyr-Yurt, about 1,500 km (930 miles) south of Moscow, Chechen regional leader Ramzan Kadyrov said.
Byutukayev is suspected of being behind a bombing that killed nearly 40 people in the arrivals hall of Domodedovo airport in 2011.
He is also accused of taking part in other attacks, including on Grozny, the Chechen capital.
The United States added him to its list of Specially Designated Global Terrorists (SDGT) in 2016.
“All underground groups in Chechnya have been completely eliminated!” Kadyrov said on social media.
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Those killed were the last militants on a federal wanted list for terrorist activity in the region, he said.
The National Anti-Terrorism Committee confirmed Byutukayev had been killed in the operation, Russian news agencies reported.
President Vladimir Putin had congratulated Kadyrov on the operation and said all those involved would receive state awards, the Kremlin spokesman said.
Chechnya, a mainly Muslim region, has been plagued with attacks on security officials and an insurgency since Moscow fought two wars with separatists after the breakup of the Soviet Union in 1991.(Reuters/NAN)
