The ONS blamed part of the fall on maintenance in a major oil field.
Compared with a year ago, total production output is estimated to have increased by 1.5%.
Output from the manufacturing sector increased by 0.2% in June, following a 0.6% drop in May.
UK manufacturers have struggled this year due to weak demand from Europe, a high pound and sluggish investment.
Despite the return to growth in June, the chief economist at the British Chambers of Commerce, David Kern, described the manufacturing sector's overall performance as "mediocre".
"Year-on-year growth is below 1% and the level of manufacturing output is still almost 5% below its pre-recession peak in the first quarter of 2008."
Chris Williamson, chief economist at research firm Markit, agreed that despite the rise in manufacturing output in June the outlook remained subdued.
"The much-vaunted UK manufacturing revival remains a distant policymakers' dream rather than a reality and the UK economy remains clearly reliant on the service sector as its primary source of growth."
He said the Bank of England's Monetary Policy Committee faced a dilemma about when to raise interest rates.
"The weakness of the (manufacturing) sector presents policymakers with a difficult decision as to whether a surging service sector justifies hiking interest rates or whether growth needs to be more balanced before the economy can safely withstand a tightening of monetary policy."
