Thousands of Celtic supporters were already making provisional arrangements to get to Windsor Park for the match which is now scheduled to take place on July 14.
A statement posted on the Celtic FC website on Friday afternoon said: ”No tickets will be available for Celtic supporters for the match. The safety and security of all Celtic supporters travelling and attending matches is of paramount importance to the Club.”
The controversial decision was taken following a meeting on Thursday morning between representatives of Linfield and Celtic and senior PSNI officers.
UEFA had directed that all of the second qualifying round first leg ties should be played on either July 11 or July 12, but it is understood the body has no objection to the new arrangements.
The timing of the match, which is near the peak of the Orange Order marching season, would have presented issues for police and security officials.