The ministry said landings at the airport were suspended until 0300 local time (0000 GMT) while authorities towed the plane from the runway.
All 89 passengers and six crew were safely evacuated from the Sukhoi Superjet 100 passenger plane operated by Azimuth Airlines from the Russian Black Sea resort of Sochi, the ministry said.
A video shared on social media by Airport Haber news website showed emergency units responding at the site of the fire, with flames and smoke coming out of the aircraft's engine.
Videos shared by the transport ministry following the incident showed the aircraft with fire extinguishing foam underneath as firefighters continue to spray the left-side engine to cool it down.
Azimuth Airlines said the plane had made a rough landing owing to wind shear. Russia's Federal Aviation Authority, Rosaviatsiya, said it was investigating the incident.
Flight tracking website FlightRadar24 said the aircraft was seven years old. Russia is short of aircraft due to Western sanctions imposed in connection with Moscow's 2022 attacks to Ukraine.