The La Liga club said in a statement that she would be replaced by fellow Singaporean and former diplomat Anil Murthy, who will step up from his current position as an executive director.
Chan was appointed in December 2014 after the club's takeover by Singaporean businessman Peter Lim amid high hopes that Valencia could once again become genuine challengers for silverware in Spain and Europe.
But after finishing fourth in 2015, Valencia could only manage 12th place last season and find themselves stuck mid table this term.
Under Chan's leadership, a succession of coaches have passed through the exit door.
Portuguese Nuno Espirito Santo left in November 2015, followed by Englishman Gary Neville who departed after four months in charge and Pako Ayestaran who lasted six.
Italian Cesare Prandelli then took the helm for three months before quitting in December with the team just four places off the bottom.
He was replaced by Salvador 'Voro' Gonzalez, who had previously had four stints as interim coach including two under Chan and who has overseen an improvement in form.
According to Valencia's website, Murthy has spent nearly 16 years' working with the Singapore government, advising ministers on trade, culture and diplomacy.
Manchester United supporter Lim bought then debt-ridden Valencia in 2014 after a failed attempt to purchase English Premier League side Liverpool four years earlier.
Valencia won the last of their six La Liga titles under Rafa Benitez in 2004, the same year as they won the old UEFA Cup, and were losing Champions League finalists in 2000 and 2001.
(Writing by Brian Homewood; editing by Richard Lough)
