The 22-year-old will not yet be back from vacation when the four-time European champions enter the competition in the third preliminary round on July 26.
"It had been previously arranged that he would go on holiday after the last game for Poland at the European Championship,” said new Ajax coach Peter Bosz in an interview on the club website (ajax.nl) on Friday.
"He badly needs a break and we are sticking to the arrangement. He was knocked out of the Euros last Friday and gets three weeks off from then."
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Milik and his Polish teammates lost on post-match penalties to Portugal in the quarter-final.
Ajax enter the competition as Dutch league runners-up and will find out the identity of their opponents at the draw in Nyon on July 15.
(Reporting by Mark Gleeson; Editing by xx; mark.gleeson@thomsonreuters.com; +27828257807; Reuters Messaging: Reuters Messaging: mark.gleeson.thomsonreuters.com@reuters.net)
