The mix-up occurred just days after the airline started to fly Airbus A321 planes along that route.
A spokesman for the carrier confirmed to the newspaper that a version of the A321 that was not certified to make long flights over water—as on the route between Los Angeles and Hawaii—was accidentally flown that day.
"We also have an ongoing, thorough review of our policies and procedures," spokesman Casey Norton told the Post. "Immediately when we realize what happened, we notified the FAA and we are working and fully cooperating with them."
American Airlines later confirmed to CNBC that the event had occurred and said that it is working to ensure something like it does not happen again.
"Nobody was really at any kind of safety risk," Michael Boyd, president of Boyd Group International, said in a CNBC "Power Lunch" interview Monday.
Nonetheless, Boyd, an aviation consultant and former American Airlines employee, added that it was in fact a "screw up" on the company's part and most likely a clerical error since it is one of the most sophisticated airlines in the world.
"American just didn't do its job right. I can guarantee you this is not going to happen again at American Airlines."
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—CNBC's Michelle Fox contributed to this report.