The museum was forced to close earlier this month after maintenance workers discovered a leak in the roof that had spread to the building's south wall. Subsequent tests revealed high levels of airborne mould.
The museum said in a statement an initial assessment showed that the work will take at least several weeks to perform and that it won't reopen before January 2015.
Staff at the museum are being redeployed to other facilities, including the Canada Aviation and Space Museum and the Canada Agriculture and Food Museum.
Museum CEO Alex Benay apologized for the closure in a statement but said the health of the museum workers and customers remain a top priority.
"We want to assure all those who support the Museum we are working with determination towards a complete, permanent solution to this unfortunate issue," said Benay.