Officers were called to the airport at around 8.10pm today (Saturday) to reports of the package.
The airport is now closed and police at the scene have put a cordon in place.
West Yorkshire Police said all passengers have been evacuated safely and the package is now being examined.
A spokesperson said: "At 8.09pm today police were called to a report of a suspicious package at Leeds Bradford Airport.ã€€
"A cordon has been put in place and the airport closed whilst the package is examined.ã€€
"Further information will be issued in due course."
At around 11pm, the airport said on its official Twitter account: "LBA terminal has been evacuated due to a security alert - more info to follow.
"West Yorkshire Police are on site and further information will be issued in due course. 2/2"