By Kevin Peachey Personal finance reporter
The building society also said property values had dropped by 1.4% compared with May as the coronavirus lockdown hit the housing market.
Sales plummeted and viewings halted when the sector was effectively frozen.
The Nationwide said the magnitude of the shock to the economy made a house price fall unsurprising.
It said the outlook for the housing market was "highly uncertain" in the coming months.
The housing market, as with the rest of the economy, has been hit hard by the coronavirus pandemic. The lockdown meant activity slowed sharply, with sales at half the levels of a year earlier.
The Nationwide, which bases its figures on its own mortgage lending, said that house prices, on an annual basis, dropped from a 1.8% rise in May to a 0.1% fall in June as the effects of the shutdown were felt. The typical home was now worth £216,403, it said.
Viewings, sales and moves have now resumed in much of the UK, but buyers and sellers face fresh unease about job and income prospects, prompting some to rethink plans over property.
"With lockdown measures due to be eased in the weeks ahead, housing market activity is likely to edge higher in the near term, albeit remaining below pre-pandemic levels. Nevertheless, the medium-term outlook for the housing market remains highly uncertain," said Robert Gardner, Nationwide's chief economist.
He said that government measures to support the economy and jobs would dilute the potential impact of the pandemic on the housing market.
What next?Prices in April, May and June were lower than the previous three months in Wales (down 2.2%) and Northern Ireland (down 0.5%) compared with rises in Scotland (up 2.5%) and England (up 0.4%), the Nationwide said. These figures can be relatively volatile owing to the relative lack of data in some areas.
Commentators said the rest of the year could be a test for the housing market.
"The property market was never going to get through such a profound economic shock without taking a material hit," said Andrew Montlake, managing director at mortgage broker Coreco.
"The second half of 2020 is going to be the real test for the property market, as government support for workers is slowly removed and we see a rise in unemployment. The government and Treasury are going to be tested like never before as they seek to keep people in jobs, which will clearly be pivotal to the future direction of house prices."