It happened on 16 September when Mr Obama visited the Centers for Disease Control and Prevention in Atlanta.
The incident came to light on Tuesday, hours after the boss of the Secret Service was grilled by Congress about a security breach at the White House.
A Secret Service official confirmed the incident but declined to comment.
The incident contravened a protocol that only members of the Secret Service are allowed to carry weapons in the presence of the president.
Tuesday's revelations led to calls from one senior US congressman for a "top-to-bottom" review of the agency.
The gun was found when the man was questioned by agents after taking a video of the president in the lift.
He was immediately sacked by his supervisors, who arrived on the scene shortly after the incident, reports said.
November 2009: A Virginia couple filming a reality show make it past Secret Service checkpoints into a dinner for visiting Indian Prime Minister Manmohan Singh without an invitation.
November 2011: A man parks a car directly south of the White House and opens fire with a rifle, striking the residence at least seven times. Secret Service supervisors fail to realise the White House has been struck for four days - until a housekeeper discovers the damage.
April 2012: Eleven Secret Service employees preparing for the president's visit to the Summit of the Americas in Cartagena, Columbia, bring sex workers back to their hotel. An altercation ensues when one agent reneges on an agreement to pay $800 (Â£500) for the night, one woman tells a newspaper. Investigators later reveal agents violated protocol by "consuming excessive amounts of alcohol and patronising questionable local establishments while off duty".
November 2013: A senior supervisor on the president's protective detail starts a row after demanding access to a woman's room at the Hay Adams Hotel overlooking the White House. He leaves behind in the room a bullet from his service weapon.
March 2014: Three agents on the elite counter assault team are sent home from the Netherlands, where they have been preparing for a presidential visit, after one is found passed out drunk in a hallway. The agents had been drinking until about 02:30 and were scheduled to be on duty at 10:00.
16 September 2014: An armed security contractor with a felony criminal record is allowed to board a lift with the president in a government building in Atlanta.
19 September 2014: Omar Gonzalez, a troubled Iraq War veteran, scales a fence at the White House, evades agents during his dash across the lawn, and enters the White House through an unlocked and unalarmed door.
A supervisor asked the man to hand over his gun, surprising the Secret Service team who had not known he was armed.
The Washington Post said the man had three convictions for assault and battery.
"This person was within arm's length of the president with a gun," said Utah congressman Jason Chaffetz, who was told of the incident by a whistleblower.
It will come as another embarrassment on the day after the director of the US Secret Service, Julia Pierson, took responsibility before a hostile House oversight committee hearing for an "unacceptable" security breach at the presidential residence.
On 19 September Omar Gonzalez, 42, scaled a fence at the White House, ran across the lawn, entered an unlocked door and was eventually tackled inside.
On Wednesday Republican congressman Michael McCaul, chairman of the House of Representatives committee with oversight of the agency, called for a comprehensive review.
"This latest episode adds to the growing list of failures from an agency plagued by operational challenges, cultural problems and reporting difficulties," he said.
President Barack Obama rode in a lift with an armed security contractor who had assault convictions, in another security lapse.