Police Scotland officers said that reports of ‘unofficial aeronautical acrobatics’ have been passed to aviation regulators.
Officers believe that three planes were seen flying past the bridge, which links the A9 from Inverness to the Black Isle, with two then reportedly flying under the bridge.
The incident is thought to have been witnessed by a number of motorists and passers-by.
Although no official description of the aircraft has been released, at least one was reportedly a biplane.
A Police Scotland spokesman said: “At around 13:13 hours on Tuesday 26 May 2015, police in Inverness received a report from a member of the public regarding an incident of possible unofficial aeronautical acrobatics when three planes were seen flying past the Kessock Bridge.
“Two of the planes were reported as having flown beneath the bridge before meeting up with the third plane and continuing on their flight path.
“Enquiries are ongoing into the matter at this time and the facts have been reported to the Civil Aviation Authority.
“If anyone has any information about the incident they are encouraged to contact Police on 101 or Crimestoppers anonymously on 0800 555 111 or online at http://www.crimestoppers-uk.org/.”
In 2003, a helicopter flew under the Skye Bridge, with people crossing the bridge stunned to see the chopper skim the water beneath them.