Warmer than usual weather curbed demand for electricity and gas, while output in the manufacturing sector continued to decline.
The Office for National Statistics said industrial output fell 1.1% in December compared with a 0.8% fall in November.
Manufacturing output fell 0.2% in December for the third month in a row.
The industrial output figures cover output in the manufacturing (the largest component of production), mining and quarrying, energy, water supply and waste management industries.
The ONS also estimated that industrial output in the fourth quarter saw a revised fall of 0.5%, as against previous estimates of a 0.2% decline.
Output from the oil and gas extraction sector fell 4.6% in December, the biggest fall since September, partly explained by the fall in Brent crude oil prices, which fell 16% in December alone and 35% in 2015 as a whole.
"The UK's economy expanded 0.5% in the fourth quarter, but this early estimate could easily be trimmed if poor construction output numbers on Friday follow the industrial data," Pantheon Macroeconomics economist Samuel Tombs said.
The second official estimate of UK economic growth in the three months to the end of December is due to be published on 25 February.
The manufacturing sector failed to contribute to UK economic growth in 2015 and the latest figures do not promise much of a recovery in 2016.
The industrial production figures come a day after the UK's annual traded goods deficit was shown to have widened to the biggest on record in 2015, at Â£125bn.
Wednesday's figures suggest the government's efforts to rebalance the economy, supported by a "march of the makers", have yet to bear fruit with Tuesday's trade figures showing a surplus of Â£90bn in services exports, primarily supported by the financial services sector.
"December's sharp drop in industrial production will fuel concerns about the UK economic outlook as well as the unbalanced nature of growth," IHS Global Insight economist Howard Archer said.
Industrial output in the UK suffered its sharpest monthly drop in three years in December, official figures show.