The average price of a UK house edged up 0.2% to £204,368 in May, but year-on-year growth slipped back to 4.7% from 4.9% in April, according to Nationwide Building Society.
Economists said uncertainty ahead of the EU referendum was already holding back house prices and warned a Brexit vote would hit the property market hard.
Activity is already easing back after a rush to secure sales before April's stamp duty hike for buy-to-let and second homes, and Nationwide said there would be a further slowdown over coming months after the first quarter lending boom.
Howard Archer, chief UK and European economist at IHS Insight, said a Brexit vote could impact activity for at least the next two years.
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He said: "A potential major downside risk to housing market activity and prices comes from the vote on EU membership on 23 June.
"A vote to leave the EU would be liable to see a marked hit to UK economic activity over the rest of this year and in 2017 amid heightened uncertainties, which would likely weigh down heavily on the housing market."
Mark Posniak, managing director at Dragonfly Property Finance, said: "What happens in June could determine the fate of the market for several years to come."
Economist Samuel Tombs, at Pantheon Macroeconomics, said the housing market would "rebound quickly" after the referendum.
Robert Gardner, chief economist at Nationwide, said: "Healthy labour market conditions and low borrowing costs are expected to underpin a steady increase in housing market activity once stamp duty-related volatility has passed, providing the economic recovery remains on track."
But he believes the recovery in activity will be gradual, with the reduction in tax relief for landlords from 2017 set to hamper the market.
"However, it is possible that the recent pattern of strong employment growth, rising real earnings, low borrowing costs and constrained supply will tilt the demand/supply balance in favour of sellers and exert upward pressure on price growth once again in the quarters ahead," he said.
The property market saw a surge in activity earlier this year ahead of the April 1 stamp duty rise, with transactions jumping to an all-time high in March - around 11% higher than before the financial crisis.
Nationwide's figures showed month-on-month house price growth shot up to 1.7% in March, while they rose 5.7% on an annual basis, which marked the biggest year-on-year increase for 13 months.