Kempes, a Valencia ambassador since 2013, has been an outspoken figure as the team have floundered this season.
After Saturday's defeat to Eibar, which left Valencia six points above the relegation zone, he said on Twitter: "Lamentably this is a team that is utterly lost. There's no style of play, no leadership and very little enthusiasm."
Hours later he announced his role with the club had been terminated. "Today I have officially been informed I am no longer the ambassador of Valencia," he said.
"But my sentiments for the club will not change, and I'll keep giving my opinions when I think things are not right."
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Kempes, who inspired Argentina to their first World Cup triumph in 1978 as top scorer, is Valencia's third highest all-time scorer.
He is a much-loved figure with Valencia supporters for his role in the team winning their first European trophy, the Cup Winners' Cup in 1980, and the 1979 King's Cup.
Valencia are the fifth most successful team in the history of Spanish soccer but are enduring one of their worst seasons in recent memory, with caretaker coach Salvador Gonzalez "Voro" the third man to take charge of the team this campaign following the departures of Pako Ayesteran and Cesare Prandelli.
(Reporting by Richard Martin; Editing by Toby Davis)
