LA Police spokesman Andy Neiman said the reports of a shooter were spurred by loud noises only, and authorities were still investigating the source.
"No shots fired, no injuries, investigation continues to locate source," Mr Neiman wrote on Twitter.
Earlier, passengers started tweeting about a security incident at the airport as posts flooded in on social media about reports of an active shooter. Videos showed passengers bolting from the airport terminal as someone yelled "get out ... run" before the sound of sirens could be heard and police cars arrived.
NBC nightly news anchor Lester Holt was caught up in the chaos.
"Arriving at LAX off flight when people started pouring out of term 4 onto Tarmac," Mr Holt wrote on Twitter.
"Security said 'shots fired. Run!'
"Now in vehicle on taxiway."
Mr Holt said witnesses told him she heard "pops" in terminal four at LAX.
"Others say they just heard 'run!'
"Those evacuated to Tarmac just allowed back in."
Police are on the scene and have urged people to remain calm.
"All precautions being taken to ensure safety of public," LA Airport PD wrote in a statement.
"Remain calm. Thank you for your co-operation."
A statement from LAX Airport later said an "individual in Zorro costume has been detained by LA Airport PD".
The man in the Zorro costume was captured on film at the airport as he was surrounded by at least six police officers with their weapons drawn and a police dog, in the time leading up to the evacuation.
"Get on the ground," one of the officers repeatedly yelled.
The man rolled off a chair, face down on the ground onto his hat and cape, before the officers moved in and handcuffed him.
"Before things got really crazy - a man in a Zorro costume with a plastic sword was arrested," the Twitter user wrote.
"Cannot confirm that Zorro man caused the ensuing chaos, but it would be one helluva coincidence."
It is not yet known if the arrest was linked to the mass evacuation at LAX International Airport.
Flights have been delayed.
