The 2012 Olympian, who ran the 100m and 4x100m relay, has been missing for over a week.
Investigators in the 31-year-old’s disappearance released a statement saying a search of the sprinter’s car showed “traces which together with other collected materials indicate a murder has been committed.
"We are combing the woods, fields and marshes in the Minsk region, but so far there are no results."
The 28-year-old suspect has been identified as a former boyfriend of the 100m and 200m national champion.
Balykina had been working as a coach since July of this year after copping a two-year doping suspension in 2013.