UK house prices were 0.1% lower in June than the same month a year ago - the first annual fall since December 2012, according to Nationwide.
Average sold prices fell 1.4 per cent month to month following a 1.7 per cent fall in May.
The government reopened the property market in mid-May after halting most sales in March as part of coronavirus lockdown measures.
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 drastically, with sales at half the levels of a year earlier.
Mortgage approvals hit a record low in May and a number of lenders, including Nationwide, have withdrawn their highest loan-to-value (LTV) mortgage offers, suggesting they are concerned prices may fall.
Robert Gardner, Nationwide’s chief economist, said it was unsurprising that prices had stalled, given the magnitude of the shock caused by Covid-19.
“Economic output fell by an unprecedented 25 per cent over the course of March and April — almost four times more than during the entire financial crisis," Gardner added.
He said that government measures to support the economy and jobs would dilute the potential impact of the pandemic on the housing market.
Gardner said that as lockdown measures eased, housing market activity was likely to edge higher in the near term, albeit remaining below pre-pandemic levels.
Despite the recent dip, average house prices are still 19 per cent higher than they were at a peak reached before the financial crash in 2007.