It was the first time that prices had fallen for three months in a row since 2009, the building society said.
Prices dropped 0.2% in May, while the annual rate of price growth slowed to 2.1% - the slowest pace for almost four years.
Nationwide said it was further evidence that the housing market was "losing momentum".
However, it said it was too early to say whether it was more than a "blip".
The building society said the slowdown could be linked to the recent squeeze on household budgets caused by the weakness of the pound.
Prices have been rising as the cost of imported goods goes up. At the same time, inflation has overtaken wage growth.
It also said "affordability pressures" in certain parts of the country could be to blame.
However, Mr Gardener said: "The number of people in work has continued to rise at a healthy pace. Indeed, the unemployment rate fell to a 42-year low in the three months to March."
He said the pressures on the market were likely to continue, exerting a drag on house price growth in the quarters ahead.
But a shortage in the supply of housing was likely to support prices, he added.
"As a result, we continue to believe that a small increase in house prices of around 2% is likely over the course of 2017 as a whole."
Property prices rose by 4.5% in 2016, according to the building society.
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, also said he expected 2% growth this year, with house prices returning to a "slowly rising path".
"Surveys suggest supply is tightening rapidly, employment growth looks set to remain steady at about 1% year-over-year, and mortgage rates still have scope to fall a little further," he said.
"But the days of surging house prices driven by sharply rising loan-to-income ratios are gone."
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UK house prices fell for the third consecutive month in May, according to the Nationwide.