The pilot, 37-year-old Gabriel Lyle Schroeder of Rosemount, Minnesota, was arrested shortly after 11:00 local time after the airport police began an investigation, Hogan said.
Before boarding, Schroeder was seen leaving a TSA control line for crew members when he noticed that additional checks had been made, the spokesman said.
"The person has left the line, causing suspicion," Hogan said. Schröder later returned to the control line and boarded the plane.
The authorities found a container of alcohol in Schröder's possession when he was taken into custody. Hogan declined to provide CNN with additional information about what kind of alcohol was confiscated.
There are currently no formal charges against Schröder. Hogan told CNN. Schroeder was booked and later released on Tuesday.
When he arrived by phone on Tuesday evening, he declined to comment on CNN.
Delta Cooperates with Authorities
In a statement released to CNN, Delta spokeswoman Kate Modolo confirmed that the airline is collaborating with local authorities.
"Delta's alcohol policy is one of the strictest in the industry, and we do not tolerate any violations." Delta cooperates with local authorities in their investigations, "the statement says.
Delta declined to provide CNN with details of the pilot's employment record and previous disciplinary issues.
When Schroeder was arrested, the plane was fully on board, but had not yet left the gate.
The passengers who boarded the plane, Delta Flight 1
"There is always a chance that the plane has started, there is a possibility," Hogan said when asked how close the plane was to departure and whether the plane could be launched.