The CAA had been investigating Twyford's use of a mobile phone after the plane doors had closed and was taxiing for take-off during a flight from Wellington to Auckland in May.
Twyford had been issued with an infringement notice for breaching CAA rules relating to the use of portable electronic devices onboard devices.
Twyford apologised and offered his resignation to Prime Minister Jacinda Ardern in relation to the incident.
He lost responsibility for the Civil Aviation Authority as a result.
"I recognise that I made the call when I shouldn't have," he previously said in a statement.