Jones is the former Liberal member of the legislature for the district of Cartwright-L'Anse au Clair.
She resigned to run for the Liberals in a federal byelection in Labrador — a race she won Monday by defeating incumbent Peter Penashue (pen-ASH'-away).
Dunderdale says she didn't want to distract voters in Labrador by calling a provincial byelection until the federal vote was over.
She says the provincial government will now move ahead as quickly as possible to fill the vacant seat.
By law, the premier has 60 days from Jones's resignation to call the byelection, and a maximum of 90 days for the vote to be held.
Lisa Dempster will be on the ballot for the Liberals when the byelection is called, while Jason Springle is running for the NDP.
The Conservatives have yet to call for nominations.