While asking rents for houses in most capital cities remained steady over the past quarter, Hobart's median weekly asking rent surged 6.8 per cent over the three months to December.

The city's annual median rent rise of 12.9 per cent brought on a $45 jump to $395 a week.

"It's the highest [quarterly and annual increase] on record for houses in Hobart," said Domain Group data scientist Nicola Powell. "It's an astounding price change that's really going to affect the budget of tenants."

Apartment rents were also up, jumping 6.3 per cent over the quarter and 13.3 per cent over the year to hit $340 a week.

By comparison, apartment rents over the quarter fell 0.9 per cent in Sydney and remained flat in Melbourne, Brisbane, Adelaide and Perth. Canberra and Darwin were the only other cities to see a rise, with respective increases of 2.4 per cent and 3.8 per cent.

Canberra and Darwin also recorded strong quarterly growth for house rents, with rises of 5.9 per cent and 5.8 per cent, but Hobart was the only city to record double digit annual growth, for apartments and houses.

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Hobart's increasing population, boosted by a return to positive interstate migration as the economy improves, is putting pressure on the rental market, said independent economist Saul Eslake, a vice chancellor's fellow at the University of Tasmania.

"The economy is picking up, there is certainly a lot more confidence in business, there is quite a lot of commercial construction and tourism is also doing well," he said. "We've had an increase in people wanting to live in Hobart ... but on the supply side there hasn't been a great deal in building approvals."

Mr Eslake said the biggest shortage was for apartments, which make up 8.6 per cent of dwellings in greater Hobart, according to the latest census data.

Demand for rentals saw Hobart's vacancy rate drop to a record low of 0.3 per cent by December, according to data from SQM Research. It now has the tightest rental market of any capital city.

The Domain Rental Report shows it also has the country's highest rental yield for houses - at 5.34 per cent for the December quarter - and the third highest yield for apartments, at 5.52 per cent.

This combined with the affordability of property in Hobart, meant investors were increasingly looking to buy there, said Simon Pressley, managing director of buyer's agency Propertyology.

"We're getting phone calls every day from people asking us to help them invest in Hobart," he said. "A lot of people are wanting to buy there, but there might only be 10 suitable properties for sale in the whole city at times."

Mr Pressley said in recent years he had bought between 80 and 90 properties in Hobart on behalf of investors across Australia.

With a lack of housing stock ensuring a steady supply of tenants, Mr Pressley said rents would continue to rise in 2018. "Absolutely nothing is surer in real estate in 2018 than Hobart rents increasing."

However, Dr Powell and Mr Eslake warned such rental growth was unsustainable.

"Don't expect to make more than 10 per cent growth [on rents] every year," Mr Eslake said. "History tells us it would be unwise to extrapolate the growth seen over last 18 months over the next few years."

Dr Powell added: "Double digit growth is unsustainable. I anticipate in 2018 that we will start to see a response to the demand for more housing and unit supply [in building approvals]."

A slowdown would be welcome news for tenants who are struggling to keep up, according to Tenants' Union of Tasmania solicitor Benedict Bartl.

"Landlords aren't afraid to jack up rents because they know they won't have any trouble getting someone new," he said. "Many tenants are paying more than they can sustainably continue to pay, but it's their only choice right now."

He noted the dwelling shortage was being exacerbated by the rise of short-term letting, which had led to an increase in landlords opting to rent their properties out as holiday homes.

"We've had several tenants, where the landlord has asked them to leave when their lease ended, then a month or two later they've seen the property up on Airbnb."