The Tiger Airways terminal at Melbourne Airport has been reopened after police conducted a search when a threat was made against the airline on Friday night.

A threat was made against the airline, grounding all outbound flights and causing incoming planes to be redirected to a different part of the terminal around 9:00pm (AEDT).

"We are responding and working with the relevant authorities over a security alert that was directed at Tigerair," a spokeswoman for the airport said.

Those already onboard a plane were stranded on the tarmac and all other flights were cancelled.

According to Melbourne Airport's website, seven Tigerair flights were due to land at the airport after 9:00pm.

Scott Marquardt, who said he was on board a Tigerair flight from Brisbane that landed about midnight, tweeted saying the crew had announced they would be on the tarmac for at least an hour.

He also tweeted that passengers were told some planes were disembarking but "we'll be on ours for a lengthy amount of time".

The terminal was declared safe about 5:00am on Saturday and the airport is now operating as normal.

The airport spokeswoman said some Tigerair flights had been disrupted but all other operations were continuing as normal.

Passengers were urged to check their website for updates.

Melbourne Airport has refused to comment on the nature of the threat.

Tigerair Australia chief executive Rob Sharp said the airline takes security alerts "extremely seriously".

"All necessary steps were taken by the airline to quickly involve the relevant authorities and implement precautionary measures to ensure passenger safety," he said.

"Tigerair apologises to affected passengers for the inconvenience and is doing everything possible to get them to their destinations as quickly as possible."