The lender urged policymakers to press on with plans to build hundreds of thousands of new homes, which it said were needed to keep pace with increasing demand and support a "sustainable increase in housing market activity".
“Surveyors have continued to report a dearth of properties on the market in recent months, with the number of available homes reportedly at the lowest level since the late 1970s," said Robert Gardner, Nationwide's chief economist.
UK house prices have continued to climb, even as growth moderates Photo: Nationwide
He described the current rate of construction activity as "well below" the rate needed to keep up with population growth.
"Only 135,000 new homes were built in England in the 12 months to September 2015, well below the c.220,000 new households that are projected to form each year over the next decade,” he said.
Despite the warning, Britain's biggest building society reported monthly house price growth of just 0.1pc in November, representing the smallest increase since June. The average house price in the UK is now £196,305, according to the lender.
On an annual basis, house price inflation moderated to 3.7pc, following October's five-month high.
While Nationwide described this as "broadly consistent with earnings growth over the longer term", it urged an increase in supply to prevent future house price inflation from running away from earnings.
George Osborne doubled the Government's housing budget in the Autumn Statement this week to £2bn a year and said it would pour more cash into a series of programmes to build 400,000 new homes across England by 2020.
The Chancellor said the policy was part of a "bold plan to back families who aspire to buy their own home", with half the homes earmarked for first-time buyers to be sold at 80pc of their market value.
Mr Gardner said it was "positive" that policymakers were "focusing on the need to increase home building".
Separately, data from the Land Registry showed the number of completed house sales in England and Wales fell 15pc to 74,596 in August, compared with 87,895 in August 2014, according to the latest available data.
The number of houses sold for over £1m also dropped 13pc to 1,280 from 1,473 a year earlier, following a hike in stamp duty to 12pc for properties worth more than £1m that was announced late last year.
The Land Registry's index is based on completed house transactions and is seen as a bellwether of sentiment in the housing market.