The Blues say they were contacted by the Football Association after an “adverse finding in a routine urine test”.
Ukraine international Mudryk denies knowingly using any banned substance and Chelsea say they will work to establish what caused the test result.
“This has come as a complete shock as I have never knowingly used any banned substances or broken any rules, and am working closely with my team to investigate how this could have happened,” Mudryk wrote on Instagram.
“I know that I have not done anything wrong and remain hopeful that I will be back on the pitch soon.”
It is unclear which banned substance was found in Mudryk’s test.
BBC Sport has contacted the Football Association for further comment.
The 23-year-old last played for Chelsea on 28 November and has missed the past five matches in all competitions.
He was included in the matchday squad for the Blues’ win against Aston Villa on 1 December but did not feature.
Head coach Enzo Maresca had said publicly that Mudryk’s absence was down to illness.
Mudryk, who signed from Ukrainian club Shakhtar Donetsk in a deal worth up to £89m in 2023, has scored 10 goals in 73 appearances for Chelsea.
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