The plane with 190 passengers on board was flying from Venice to Moscow Vnukovo airport.
"The aircraft reported an engine failure and requested an emergency landing at the closest airport in Minsk," Xenia Perestoronina said.
"The plane landed safely at about 12.45 Moscow time (10.45 GMT)," she said. "No injuries were reported among the passengers."
An additional plane has been dispatched by the airline to deliver the passengers to Moscow.
Red Wings was established in 1999 under the name VARZ-400 after the Vnukovo Avia Repair Factory (abbreviated VARZ in Russian). It was renamed Airlines 400 in 2001, before being assigned its current name in 2007.
It is owned by Russian tycoon Alexander Lebedev who decided to create a small discounter airline using modern Tu-204-100 aircraft.
The airline operates four Tu-204 and two Tu-154M planes and provides both scheduled passenger and cargo charter services.