She became fully unresponsive at 11:47 p.m., according to the Review-Journal.
No incidents happened while the woman, who was heard in recordings slurring words, possibly lost consciousness just before midnight Wednesday, according to the FAA, the AP reported.
Recordings show that commercial pilots could not understand her as she gave directions for landing, takeoff and taxiing at McCarran International Airport.
Pilots were even heard discussing among themselves about something being wrong.
The woman is also heard apologizing over the radio, telling those listening that she was "choking a little bit." Then she misspoke an aircraft's call numbers. Her microphone also picked up her coughing and grunting, the AP reported.
Eventually another air traffic controller who was on break was told to return to the tower at 11:50 p.m. after pilots told controllers at the Las Vegas approach control, the Review-Journal reported. He started dealing with air traffic four minutes later. The approach control is at the base of the main tower, but is a separate operation.
Paramedics were also called, the AP reported.
The woman was put on administrative leave and the FAA said that two controllers must be in the tower during busy hours, the AP reported.
The woman had been alone while her co-worker was on break.