Magomed Yevloyev died in hospital in the republic's largest city of Nazran.
A source in the republic's Interior Ministry told RIA Novosti that Yevloyev's death had come about after he was detained by police at Magas Airport. Police officers then put him in a police car to take him to Nazran to give testimony regarding "a criminal case."
"Preliminary reports say that as the vehicle that Yevloev and the police officers were in was moving, one of the police officers' guns accidentally went off, and a bullet hit Yevloyev in the head," the source said.
"He was shot straight in the temple," said Magomed Khazbiyev, Yevloyev's official representative, adding that doctors had done all they could to save his life.
Yevloyev's website was closed down earlier this year after being labeled extremist. Local authorities said that the website had called on people to take part in unsanctioned demonstrations in January. The protests against the local administration were banned over public safety fears. The decision to close the website was approved by a Moscow court earlier in August.