Rigoberto Alpizar, a 44-year-old US citizen, was shot after fleeing an air marshal. No device has been found.
Alpizar had arrived in Miami, Florida, from Ecuador and was boarding a flight to Orlando.
It is the first time since the attacks of 11 September 2001 that a US air marshal has shot at a passenger.
The US dramatically increased the number of air marshals on flights after the 2001 attacks.
