The doors had already opened for the show and the Ziggo Dome was full.
According to the promoter, the Canadian rapper was advised not to perform by a doctor after falling ill.
"I'm really sorry to tell you that tonight's gig cannot take place. Drake got sick. His doctor told him not to perform."
The postponed show has been moved to Wednesday night instead.
This is the third time the Amsterdam show has been cancelled.
His performances on 20 and 21 January were initially moved to 26 and 27 January. But they were postponed again until 27 and 28 March.