The man, identified as 41-year-old Phani Kumar Varanasi, had entered into a secure area of Terminal B at the airport through a guarded exit on May 23. He told police that he was confused about where to go and had wandered into the restricted area at the terminal.
His trespassing had caused a security scare and led to evacuation of the busy terminal, a report in the New York Daily News said.
The Transportation Security Administration (TSA) said Varanasi, who has no criminal record, spent five minutes in the "sterile area" before returning to the public space through the same exit.
The report said Varanasi, a general manager at an India-based manufacturing firm, was flying into New York from Detroit when the incident occurred.
He was identified by police through surveillance video and a list of passengers aboard the flight. A video obtained by the Daily News showed Varanasi walking directly past a TSA security employee at a desk.
Varanasi was due in Queens Criminal Court for a hearing on a criminal trespass charge, the report added.
Republican lawmaker Peter King called for a full investigation and explanation of how Varanasi was able to walk unchecked through a security guard from the airport's baggage claim to the off-limits area.
"We have to be constantly on our guard, and the breach at LaGuardia has to be explained and corrected," King tweeted.
The report also said that police contacted Varanasi to come in for an interview at LaGuardia and arrested him after he voluntarily appeared.