The CAA had agreed to close the skies over the hotel in northern Israel.
However, Transport Minister Yisrael Katz then threatened to sack the CAA boss if he did not overturn that decision.
In the end, the skies stayed open to all air traffic during Thursday’s wedding, Israeli media reported.
Bar Refaeli, 30, Israel’s most famous supermodel, married billionaire Israeli businessman Adi Ezra at the Carmel Forest resort near Haifa.
According to Israeli media reports, Bar Refaeli and Adi Ezra were planning to have five drones, two helicopters and an observation balloon circling the venue, some for photographic purposes.
The CAA initially agreed to the couple’s request for a ban, citing safety reasons.
However, Minister Yisrael Katz on September 20 overturned that decision saying: “The skies belong to all Israeli citizens and we can’t offer special treatment for this event over other events.”
Israeli pilots had also objected to the ban.
On September 22, according to Israeli media, the CAA, appearing to disregard Yisrael Katz’s comments, announced a no-fly zone would be in place for safety reasons from 17:00 on September 24 to 02:00 on September 25.
Yisrael Katz reportedly told CAA chief Joel Feldschuh: “If the skies are not open above Bar Refaeli’s wedding – you will be removed from your post.”
On Thursday evening the transport ministry told The Jerusalem Post that the skies had stayed open to all air traffic.
The Times of Israel reported the rabbi was flown in by helicopter for the ceremony.
Forbes Israel has ranked Bar Refaeli as Israel’s top-earning model reporting revenue of nearly $16 million in 2013 when she appeared in a lucrative Super Bowl advert.
She has hosted Israeli X Factor and modeled for brands including Desigual and Escada.
A former girlfriend of actor Leonardo DiCaprio, Bar Refaeli prompted criticism in 2003 when it was reported she had opted not to finish her compulsory military service.
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