The message sent to mobile phones warned, in capital letters: "Ballistic missile threat inbound to Hawaii. Seek immediate shelter. This is not a drill."
A video on social media showed the emergency system interrupting the broadcast of a football match, with a high-pitched sound alerting viewers to their screens which displayed the same warning.
The message, which was sent at 8.07am local time (6.07pm GMT), was followed by a retraction 38 minutes later stating the missile alert was a "false alarm".
David Ige, the governor of Hawaii, said the accidental alert was "unfortunate" and "regrettable" and apologised to Hawaiians.
"It was a mistake made during a standard procedure at the change over of a shift, and an employee pushed the wrong button," he explained.
A spokesperson for the White House said that President Trump had been briefed on the alarm. "This was purely a state exercise," they said.
The US military's Pacific Command also said there was no ballistic missile threat to Hawaii.
Hawaiian Senator Brian Schatz said on Twitter: "There is no missile threat. It was a false alarm based on a human error.
"There is nothing more important to Hawaii than professionalizing and fool-proofing this process."
"Again false alarm," he wrote in all capitals.
"What happened today is totally inexcusable. The whole state was terrified. There needs to be tough and quick accountability and a fixed process."
According to social media reports, the alert sent many of the islanders into a panic.
The message seems to have been sent as part of the US Wireless Emergency Alerts (WEA) system, which allows authorised national, state or local government authorities to send alerts regarding public safety emergencies.
Last December, the Pacific island tested sirens warning of an impending nuclear attack from North Korea.
Hawaii had been named as a potential target of an intercontinental ballistic missile launched by Kim Jong Un, who has threatened the US with a nuclear strike.
Officials in Hawaii have spent months briefing the public on what action to take in the event of an attack. It is estimated that Hawaiians would have less than 20 minutes before the missile arrived.(c) Sky News 2018: Hawaii accidentally warns citizens of incoming missile