In a statement, the nation's Centers for Disease Control said the Kiwi pilot tested positive for the virus on December 20, after flying between Taiwan and the US.
The agency said the pilot, in an initial interview, could not recall all activities and didn't mention a contact history with the new case.
The health agency also said a failure to provide truthful contact information could violate the Infectious Disease Prevention and Control Law and result in fines of up to NT$300,000 (NZ$15,000).
At the same time, the CDC's Central Epidemic Command Center also announced three new confirmed cases of Covid-19 imported from abroad.
All of the imported cases arrived from the Philippines.
It is Taiwan's first locally transmitted case of Covid-19 in eight months.
The government was jolted by Tuesday's announcement of the domestic infection of a woman who is a friend of a New Zealand pilot confirmed to have been infected earlier this week.
The case has angered Taiwanese locals, with one Taiwan television network labelling the Kiwi pilot a "public enemy".
They claim he did not report all his contacts and places he had been and failed to wear a face mask in the cockpit.
In a meeting of its disciplinary committee, EVA Air decided to terminate the pilot's contract, effective immediately, saying he had breached government regulations and the communicable disease transmission law.
"EVA Air has always abided by the government's epidemic prevention policies, and most crew members also followed the epidemic prevention regulations," it said.
"However, the behaviour of an individual employee has undermined everyone's efforts at epidemic prevention."
The pilot is currently being treated in hospital.
According to Channel News Asia's (CNA) English-language news website Focus Taiwan, the pilot has since been fined NZ$15,000 for the incident.
Taiwan, which has a population of more than 23 million people, has reported just a total of 777 Covid-19 cases – mostly imported – and seven related deaths.
