Thousands of people have been killed across the Middle East since the US and Israel attacked Iran on February 28 and Iran launched strikes against Israel, US bases and Gulf states.
The last-16 encounters had originally been scheduled to be played in Qatar, Iran, Saudi Arabia and the United Arab Emirates on a home-and-away basis in the first two weeks of March.
Defending champions Al Ahli are due to take on Al Duhail from Qatar while four-times winners Al Hilal face Al Sadd. Shabab Al-Ahli from the UAE play Iran's Tractor FC and Al-Wahda meet Saudi Pro League champions Al Ittihad.
Those fixtures will now be held on April 13 and 14 as single-leg ties ahead of the tournament's finals stage.
Jeddah had already been slated to host the quarter-finals, semis and final on a centralised basis with matches running from April 16 to 25.
Last-16 matches on the Eastern side of the draw have already been concluded, with Japanese pair Vissel Kobe and Machida Zelvia joined in the quarter-finals by Thailand's Buriram United and Johor Darul Ta'zim from Malaysia.
The draw for the quarter-finals will be conducted in Kuala Lumpur on Wednesday.