The 0.2% rise in house prices last month was down from a 0.8% rise in December, although that left prices 4.3% higher than at this time in 2016.
"The outlook for the housing market remains clouded," said Nationwide economist Robert Gardner.
The average price of a house in the UK dropped slightly to Â£205,240.
Mr Gardner said that so far there had not been a negative impact on the economy following the vote to leave the EU.
"The economy has remained far stronger than expected in the wake of the Brexit vote.
"Recent data indicates that the economy didn't slow in the second half of 2016 and the unemployment rate remained stable at an 11-year-low in the three months to November."
However, he added: "There are tentative signs that conditions may be about to soften.
"Employment growth has moderated and while wage growth has edged up in recent months, in real terms, earnings growth has already slowed."
Even though the Nationwide reckons that house price inflation was 4.3% in January, it still believes the average figure for 2017 will end up at 2%. That implies a fairly dramatic dip in inflation during the months ahead.
In fact it looks like house prices could soon be rising at a slower rate than the cost of living as a whole.
In the smartest parts of London, prices have already fallen by up to 12% in the last year, according to some analysis.
But Nationwide's gloomy outlook for the economy and house prices may be good news for house-hunters.
Annual UK house price inflation fell to its weakest level since November 2015 in January, according to mortgage lender Nationwide.