The 27-year-old, who has spent his entire senior career in Spain, was scrutinized by the country's authorities after comments made by his father before the World Cup.
Cheryshev Sr. said in an interview his son had received growth hormone treatment prior to the tournament, but later insisted he had been misquoted.
The former Real Madrid man, who is on loan at Valencia from fellow La Liga side Villarreal, tweeted an image from AEPSAD on Thursday explaining his case had been archived after no evidence of irregularities were found.
Cheryshev, who had 11 caps and no goals for Russia heading into the World Cup, scored four times in five games during the tournament as the home nation reached the quarterfinal. He also netted in the 2-1 Nations League B win over Turkey last week and has one goal in 95 minutes of football for Valencia so far in 2018-19.