The 22-year-old Trinidad and Tobago international was substituted in the 94th minute of their league victory in Budapest, and was later taken to hospital after feeling dizzy.
Adams was making his sixth appearance for the club in their city derby having signed for the club earlier this year, but began to feel unwell following the victory that saw his team rise to second in the league table.
"During last night, Akeem Adams suffered a heart attack," club communications director Zoltan Vamos confirmed on the club's official website.
"The player was taken to hospital where he received immediate professional care.
"Doctors are still struggling to stabilize his condition.
"The news is a shock to the technical staff, the players and the club's staff.
"Akeem Adams is fighting for his life."
The club also confirmed that Adams had undergone medical examinations as required by FIFA and UEFA and no problems were evident from his tests.
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