However, annual growth remained stable at 4.4% compared with the figure of 4.5% the previous month.
The average price of a property is now £196,829, slightly down on December.
But Nationwide warned the demand for homes was likely to strengthen in the coming months, as a result of a strong labour market, combined with wages going up at a “healthy pace” and the prospect of interest rates remaining at 0.5% for longer than previously expected.
“The concern remains that construction activity will lag behind strengthening demand,” said Nationwide’s chief economist, Robert Gardner, “putting upward pressure on house prices and eventually reducing affordability.”
He also highlighted the Royal Institution of Chartered Surveyors report that the number of properties on estate agents’ books is close to its lowest level.
The figures come as the boss of one of the UK’s largest insurers, and one of the biggest investors in infrastructure in the UK, said the country was “obsessed” with rising house prices.
Nigel Wilson, chief executive of Legal and General, told BBC Radio 5 live: “We are obsessed with owning homes, we are obsessed with house price inflation which is socially exclusive, which isn’t good for society and is very poor for young people finding it increasingly difficult to get on the housing ladder.”
Separate figures show that mortgage lending by the major High Street banks picked up pace at the end of last year.
The British Bankers’ Association (BBA) said that gross mortgage borrowing of £12.4bn in December was 24% higher than the same month a year earlier.
Overall, new borrowing in 2015 was 6% higher than the previous year.
Mark Harris, chief executive of mortgage broker SPF Private Clients, said: “Cheap mortgage rates have certainly helped fuel the growth in lending in the market seen throughout 2015. However, we have probably seen the back of the very cheapest deals.
“The biggest issue for many is actually qualifying for one of these great mortgage deals.”