"Negative results led the two parties to accept the consequences," a club statement said on Monday.
Jankovic, a former Red Star Belgrade coach, took over the ten-time Belgian champions in September 2016.
A former assistant and youth coach at the club Jose Jeunechamps will oversee the end of the play-offs, in which Standard have also struggled.
The club said a new coach would be hired before the start of next season.
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