The Yediot Ahronot daily said a plane with 50 people on board circled over Israel on Monday, with the passengers chanting prayers and sounding the ritual ram's horn.
The newspaper report carried a photo showing bearded and black-clad Orthodox Jewish men standing on the steps of an aircraft of Israeli short-haul airline Arkia. Airline officials could not be reached for comment.
"The purpose of the flight was to stop the (swine flu) epidemic so that people will not keeping dying from it," Rabbi Yitzhak Basri, one of the participants, told the newspaper.
Israel's Health Ministry has confirmed more than 2,000 cases of swine flu, with five fatalities in the country so far.
Warnings have been issued of widespread infections in Israel in the fall and winter, and Israeli Prime Minister Benjamin Netanyahu has pledged to obtain enough vaccine to protect every Israeli citizen from swine flu.