Cricket and soccer organisations are also keeping a close eye on developments as missile strikes continued to rock the region on Saturday after US and Israeli forces attacked Iran, with Iranian retaliatory attacks reported in Dubai, Doha, Bahrain and elsewhere.
Formula One's European-based teams were set to be heading to Melbourne for next weekend's season-opener via the Middle East, meaning an overhaul to their flights.
Next Sunday's race is expected to go ahead unaffected, but the Bahrain and Saudi Arabia Grand Prix, the fourth and fifth rounds of the new campaign, are set for April 12 and 19.
An F1 spokesperson said: "Our next three races are in Australia, China and Japan and not in the Middle East - those races are not for a number of weeks.
"As always, we closely monitor any situation like this and work closely with relevant authorities."
Football's governing body FIFA is monitoring events just months before the start of World Cup in the US, Canada and Mexico in June. Iran have qualified and are scheduled to play two matches in the US, in Los Angeles and Seattle.
FIFA secretary general Mattias Grafstrom told the International Football Association Board's annual meeting in Cardiff: "We had a meeting today and it is premature to comment in detail, but we will monitor developments around all issues around the world.
"We will continue to communicate as we always do with three host governments as we always do in any case. Everybody will be safe."
A cricket match between England Lions and Pakistan Shaheens, scheduled for Sunday in Abu Dhabi, has been cancelled, the England and Wales Cricket Board (ECB) also reported.
"The safety and security of our teams and staff is our top priority," the ECB said in a statement, adding that England women's planned trip to Abu Dhabi next week had been delayed.
Cricket's governing body (ICC), headquartered in Dubai, earlier said they had activated contingency plans for their personnel, who were scheduled to transit through Dubai for onward travel to their home countries.
"We would also urge fans who have travelled ... to monitor closely and adhere to advisories being issued and consider all factors before undertaking any further international travel," an ICC spokesperson said in a statement.
The Asian Football Confederation (AFC) on Sunday postponed Asian Champions League Elite round-of-16 games in the west region that were scheduled for Monday and Tuesday.
East region games, such as Melbourne City's ACL Elite round-of-16 home first leg against Buriram United on Tuesday, will proceed as planned.
ACL Two and AFC Challenge League quarter-final matches in the west region this week were also postponed.
Professional Footballers Australia (the PFA) are working with FIFA, the AFC and the Australian government to support players in the region.
"The PFA is in the process of reaching out to all impacted players to ensure they are safe and supported," PFA chief executive Beau Busch said in a statement provided to AAP.
There are few Australian footballers currently based in the Middle East, with one-cap Socceroo Connor Pain, who plays for Saudi second-tier club Al-Bukiryah, among them.
Iran's women's football team are on the Gold Coast ahead of playing South Korea in their Asian Cup opening match on Monday.
A question regarding the team's reaction to the killing of Iran supreme leader Ayatollah Ali Khamenei on Sunday was shut down in the pre-match press conference.
With agencies
