A woman who told staff at the check-in counter at Hobart Airport she had explosives in her luggage was allowed through security screening and boarded the aircraft before security staff removed her from the plane.

The 41-year-old, from Knoxfield in Victoria, has been charged with making false threats and is due to appear in court in Hobart in an out-of-hours session.

Police allege she made the remarks at the Virgin Airlines check-in counter on Friday afternoon.

The ABC understands the woman was attempting to board a flight to Melbourne.

In a statement, police said while at the counter the woman was "spoken to by airline staff, and again on the tarmac".

"The woman was then removed from the flight by airport security and police were notified," police said.

Police said the woman told them she made the remarks "as a joke".

Measures then had to be taken to "rule out a bomb threat and ensure airline staff and passenger safety", police said.

The flight was delayed for an hour while those checks were made, they said.

Australian Federal Police officers were removed from the Hobart Airport in October 2014, after a $22-million Commonwealth budget cut.

Virgin has been contacted for comment.