Magomed Yevloyev, owner of the Ingushetiya.ru site, was a vocal critic of the region's Kremlin-backed administration.
The Russian prosecutor's office said an investigation into the death had been launched, Interfax reported.
A post on Yevloyev's site said he was detained at Ingushetia's airport.
The website owner was taken to hospital but died from his injuries.
Reports quoting local police said Yevloyev tried to seize a policeman's gun when he was being led to a vehicle. A shot was fired and Yevloyev was injured in the head.
Human rights concerns
The predominantly Muslim province borders Chechnya and has suffered from overflowing unrest.
There is a low-level insurgency, with regular small-scale ambushes against police and soldiers.
In June 2008, the Human Rights Watch group accused Russian security forces there of carrying out widespread human rights abuses.
HRW said it had documented dozens of arbitrary detentions, disappearances, acts of torture and extra-judicial executions.