The local Safety Advisory Group (SAG) covering Villa Park in Birmingham last week blocked visiting fans from attending the 6 November match following a police risk assessment.
That decision drew political criticism, including from UK Prime Minister Keir Starmer, with calls for the ruling to be reversed. The government said on Friday that it was working to allow Israeli fans to be present.
But a statement on the Maccabi Tel Aviv website said: "The well-being and safety of our fans is paramount and, from hard lessons learned, we have taken the decision to decline any allocation offered on behalf of away fans, and our decision should be understood in that context.
"We hope that circumstances will change and look forward to being able to play in Birmingham in a sporting environment in the near future."
The announcement came only a day after Israeli police called off the Israeli Premier League match between Maccabi and city rivals Hapoel because of 'riots' reported between rival fans.