Both countries have been struck during Iran's response after the United States and Israel launched a wave of attacks on Iran.
The announcement was made early on Sunday morning in Shanghai ahead of the Chinese Grand Prix.
F1 was due to race in Bahrain on April 12 and Saudi Arabia on April 19.
"The FIA will always place the safety and well being of our community and colleagues first. After careful consideration, we have taken this decision with that responsibility firmly in mind," FIA president Mohammed Ben Sulayem said.
The FIA didn't explicitly rule out rescheduling the races, and Ben Sulayem said: "Bahrain and Saudi Arabia are incredibly important to the ecosystem of our racing season, and I look forward to returning to both as soon as circumstances allow."
F1's packed schedule doesn't have any obvious open dates for rescheduled races this year.
Calling off the Bahrain and Saudi Arabian races means there will be a five-week gap from the Japanese Grand Prix on March 29 and the next race, the Miami Grand Prix on May 3. Without any rescheduling, the 22-race schedule would be the shortest since 2023.
The two Middle East races weren't until next month but F1 faced making a decision earlier because it typically flies in the first staff and cargo to tracks weeks in advance. F1 was also faced with the difficulty of selling tickets at short notice, which make it almost impossible to set up a replacement race in other countries.
Kimi Antonelli, the Mercedes driver who qualified on pole position for Sunday's race in Shanghai, said his thoughts were "with the ones that are suffering from this situation" and that safety needed to be the priority, adding of the FIA and F1: "I'm sure they will do the right thing."
Bahrain had already hosted two pre-season F1 tests before Israel and the US launched attacks on Iran. A smaller-scale test of wet-weather tires was called off in the immediate aftermath of those strikes.
A travel shutdown affecting major airports in the Middle East also caused disruption for Europe-based F1 and team staff heading to Melbourne for the season-opening Australian Grand Prix.
The last time a scheduled F1 race was cancelled was in 2023, when the Emilia Romagna Grand Prix in northern Italy was called off at short notice due to deadly floods in the area.
In 2022, F1 continued with its race weekend in Saudi Arabia even after Yemen's Houthi rebels attacked an oil depot during a practice session, with black smoke visible from the Jeddah circuit.
The same year, F1 cancelled the Russian Grand Prix's contract after Russia invaded neighbouring Ukraine.
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