The Italian left the Gulf country to attend to “a family medical matter," the club said in a statement.
"Following the recent developments in the region, Mancini departed as scheduled. However, due to the flight situation, he has not yet been able to return."
The United States and Israel have launched strikes on Iran since February 28th, triggering a region-wide conflict as Tehran attacked Israel and Gulf countries.
Air travel has been disrupted since, with several sporting events scheduled in the region being postponed, including some AFC Champions League Elite round-of-16 games.
In Mancini's absence, Sergio Alegre will guide Al-Sadd.
Qatar had halted all sports competitions on March 1st after Iranian missile and drone strikes prompted authorities to close the country's airspace.
“Coordination will continue for the coach's return at the earliest available opportunity," the club added.