The RIA news agency cited Russia's United Aircraft Corporation (UAC), which makes the plane, as saying the incident took place during a training flight in the Khabarovsk Region and that the pilot ejected safely.
The Defence Ministry will set up a commission to investigate the accident, which looked like it was caused by a failure in the steering system, the TASS news agency cited two military sources as saying.
The lost plane was one of the first to be mass-produced and was due to be handed over to the Russian air force by the end of this year, the Interfax news agency reported, citing a source.
Russia has previously tested the Su-57 in Syria.
A prototype of the plane, conceived as a rival for the US F-22 Raptor, first took to the skies in January 2010. The Su-57 made its first appearance at Russia's annual Red Square parade in May last year when a pair of them roared over Moscow.