The contest between European Championship winners Spain and Copa America champions Argentina was scheduled for March 27th at Doha's Lusail Stadium, with potential big-name draws including Lamine Yamal and Lionel Messi.
"Qatar Football Association announces the postponement of all tournaments, competitions and matches, effective from today and until further notice," the association said in a statement on Sunday.
"The new dates for the resumption of competitions will be announced in due course through the Association's official channels."
The final call on whether to postpone the game rests with event organisers UEFA and CONMEBOL.
The Bahrain Football Association postponed all its matches until further notice, while the Asian Football Confederation on Sunday announced it was delaying Champions League Elite fixtures in the region.
The Asian Champions League Two, currently at the quarter-final stage, has also been impacted, along with games in the Challenge League.
Countries across the Middle East have been on high alert since Saturday, when the US and Israel launched air strikes against Iran, aimed at diminishing Iran's military capability.
Iran retaliated by attacking US targets around the region, including in the UAE, Saudi Arabia and Qatar.
On Sunday, Qatar's interior ministry reported a fire in an industrial zone after debris fell from an intercepted missile.