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.