The 35-year-old has been awaiting action since making himself unavailable for the Ukrainian outfit since the 2-1 win over Napoli in September.
Srna was found by the National Anti-Doping Center of Ukraine (NADCU) to have had DHEA - which occurs naturally in humans - in his system, though an "atypical" amount was discovered in the sample.
However, the former Croatia captain will be given the green light to return in August as the suspension is backdated to when he failed the test.
"Mr Srna acknowledged that he had violated (unintentionally) anti-doping rules," a statement from the NADCU read.
"After examining the source of the adverse result of the analysis, NADC took note of Mr Srna's explanation of the circumstances that preceded the testing, and concluded that there was no significant guilty or negligence of the athlete in the violation."
Srna has spent the last 15 years in Ukraine with Shakhtar, racking up close to 350 league appearances during that time.