A large bushfire burning near suburbs and towns in southern Tasmania is likely to continue for another week, authorities say.

The 1900-hectare fire at Molesworth, northwest of Hobart, continued to burn out-of-control on Saturday.

No serious damage has been reported, but a watch and act message was in place.

The fire sent a thick blanket of smoke across Hobart, forcing the closure of all walking tracks and roads on Mount Wellington.

Tasmania Fire Service Chief Officer Mike Brown urged residents in the city's northern suburbs to be prepared for any escalation in coming days.

"People living in bushfire prone areas, including those living on the city fringes of Glenorchy and Hobart, need to remain vigilant and be very much aware of what is going on around them," Mr Brown said.

"People need to be prepared to act quickly and all family members need to be familiar with their bushfire survival plan."

He said the Molesworth fire, as well as a 1500-hectare fire at Fingal, in the state's north east, could burn for another week before being brought under control.