Standard, winners of the Belgian league 10 times, finished ninth in the regular phase of the season.
As a result they missed out on securing a place in next season's Champions League. The clubs which finished in the top six during regular season battle it out during the playoffs to secure Champions League places.
"The negative results led the two parties to draw the consequences," Standard said on their website.
The club said Jeunechamps would take over until a new coach was found by the start of next season.
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Jeunechamps, 49, previously worked at Belgian second division club RFC Seraing and as an assistant manager at Standard and English side Charlton Athletic.
(Reporting by Robert-Jan Bartunek, editing by Pritha Sarkar)
