The Office for National Statistics (ONS) said output slumped in the run up to the European Union (EU) referendum.
The fall was almost a complete reversal of April's 2.8% rise in construction activity.
Construction output, which accounts 6% of economic growth, will have to expand by 1.9% in June to avoid dragging on the wider economy, the ONS said.
But the chances of that happening look slim given the the private sector data already released.
Housing construction output fell 3.2% in May after edging down 0.1% in April, the biggest drop since February 2014.
Housing output has now fallen in every month this year apart from February.
"The fall in May 2016, taken together with the strength of April's figures, continues a longer trend of broadly flat output growth since the start of 2015," the ONS said.
On an annual basis construction output fell 1.9% compared with May 2015.
The most recent figures from the ONS showed UK economic growth slowed to 0.4% in the three months to the end of March.
The first estimate of second quarter economic growth is due on 27 July.
Financial firm Markit, which has given an estimate of construction activity in June, said the weakness had continued into last month.
It said the industry suffered its worst contraction in seven years in June as concern grew about the EU referendum.
Howard Archer, chief UK and European economist at IHS Markit said the figures showed the construction sector was "hit appreciably by increased caution among clients  as the run-up to the referendum on EU membership magnified UK and global economic uncertainties".
Mr Archer added: "This immediately raises serious concerns as to just how much the construction sector will be hampered by the Brexit vote."
Construction output fell by 2.1% in May compared with a month earlier, official figures have shown.