While in the restaurant, the boy is reported to have asked a waiter to watch the bag while he went to the lavatory. However, he did not return.
The incident was reported to the Transportation Security Administration, whose gate agents screened the boy for security before allowing him into the departure area.
It was also reported to the Minneapolis police and the Hennepin County attorney's office.
The boy was returned to the Minneapolis-St Paul area. His parents are reported to be co-operating with investigators.
A spokesman for Delta said: "We are investigating the incident and co-operating with the agencies involved." A spokesman for the airport stressed: "This is a rare incident."