Pinter was appointed as Sandor Egervari's successor in December after Hungary missed out on qualifying for the World Cup play-offs.
Former Hungary international Pinter took charge of five games in total during his reign and won only twice - friendly wins over Albania and Kazakhstan in June.
However, his only competitive international in charge ended in a 2-1 Euro 2016 qualifying defeat to Northern Ireland in Budapest earlier this month.
Goals in the final 10 minutes from Niall McGinn and Kyle Lafferty sent the visitors home with the three points in what proved to be Pinter's final game in charge.
Former Hungary international Pal Dardai will take over on an interim basis for the remainder of the year, taking charge of qualifers against Romania, the Faroe Islands and Finland.
Dardai, 38, currently helps to coach youth teams at Bundeslia side Hertha Berlin.