The Gunners were due to take on the Eredivisie giants in the Europa League on Thursday night, a contest that was set to take place at the Emirates Stadium in north London.
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UEFA confirmed on Monday that the tie would not now be played and that a new date for the match would be communicated in due course.
European football's governing body said the postponement was due "to the severe limitations on police resources and organisational issues."
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This is due to plans for the state funeral for Her late Majesty, Queen Elizabeth II, who passed away last week at the age of 96, which will take place next Monday.
The Queen's coffin will also be lying in state in Westminster from Wednesday where it is expected mourners could queue for five miles to pay their respects.
Arsenal released a statement which read: "The postponement follows liaison between UEFA, the Metropolitan Police and ourselves, after the passing of Her Majesty Queen Elizabeth II.
"We are working with the authorities to reschedule the match and any tickets purchased for this fixture will be valid for the rescheduled date."
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The decision comes after it was revealed that Champions League fixtures on Tuesday and Wednesday night would go ahead, while EFL matches will also resume this week.
The postponement of a match in London on Thursday, though, would appear to place serious doubt over Premier League matches taking place in the capital on Saturday and Sunday.
In the Premier League, Tottenham are due to host Leicester on Saturday evening while Brentford host Arsenal and Chelsea are at home to Liverpool on Sunday.