The system-wide ground delay is in place until at least 4 p.m. ET, the airline tweeted.
All fights on the ground will be held at their gates until the computer glitch is fixed. Planes in the air were allowed to land, NBC News reported.
"American's reservation system is experiencing intermittent outages," American Airlines spokesperson Andrea Huguely told NBC. "We're working to resolve the issue as quickly as we can."
The airline later tweeted it was "unable to modify today's reservations," but offered refunds or updated travel at no charge.
Many passengers used social media to flood the airline with complaints.
American estimates it flies about 275,000 passengers a day and receives more than 239,000 reservations calls, according to CNN.