The Piper PA-31P took off from the airport Thursday morning.
The pilot was attempting to return to the airport when the plane crashed in a grassy area some 50 yards from commercial buildings adjacent to the airport grounds.
KGNS-TV in Laredo reported earlier that the plane caught on fire.
Laredo police spokesman Joe Baeza says the airport was closed to all commercial and cargo air traffic following the wreck.
No other people were aboard the plane beyond the three who were killed.
Their identities have not been released.
Federal Aviation Administration records show the Piper is registered to a man in Bruni, a small community east of Laredo.
Baeza did not know the plane's destination.
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