Individually, there were slower increases in output, new orders and employment.
A reading above 50 indicates expansion while that below shows contraction in the sector.
Order growth in January also slowed and t he weak pound continued to have an inflationary impact, with purchasing costs rising at the strongest rate for nearly eight and a half years as suppliers passed on higher prices for commodities and imported construction materials.
The final Markit Eurozone Manufacturing Purchasing Managers' Index (PMI), based on survey data from approximately 3,000 manufacturing firms, rose to 55.2 in January from 54.9 in December, and above an earlier flash estimate of 55.1, Markit said.
The latest PMI value signaled a material improvement in the health of Taiwan's manufacturing sector, which might continue to expand in the coming months, the monthly survey sponsored by the Japanese media organization and conducted by London-based IHS Markit showed.
That's down from 56.2 in December, although it remains well above the boom-or-bust line of 50 that separates expansion from contraction.
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It added that employment remained in growth territory for the fifth consecutive month, which the job creation rate eased further from November's 13-month high and was only marginal overall.
With "signs of demand running ahead of supply", there are hints of a "tentative build-up of core inflationary pressures", said Chris Williamson, chief business economist at IHS Markit.
"The major emerging concern - particularly among the more energy-intensive manufacturers - is the deteriorating energy price outlook which threatens to stifle the tentative recovery underway in the sector", Mr Willox said in a statement.
"A continued welcome increase in new orders, primarily from domestic sources, as well as overseas, has meant that the UK Manufacturing PMI has seen continuous growth for the last six months, which is great news for UK manufacturers and the economy".
Yet according to the latest PMI, manufacturing orders from overseas rose at the weakest since last May, following a surge in the second half of 2016.