Growth in both new orders and output in the sector fell since May, when the PMI reading was 52.2.
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It does, however, mark the twelfth month in a row of growth in the sector, with a reading over 50 marking expansion.
Manufacturing conditions in the euro zone were brightest in Spain and Ireland, where activity hit an 84-month high and 2-month high respectively. Meanwhile in the U.K., which is not part of the currency bloc, June's manufacturing PMI rose to 57.5 - the highest level since November 2013.
However activity continued to contract in France, the euro zone second-largest economy, where it fell to a six-month low of 48.2. France has been dubbed the "sick man of Europe" by some analysts, after economic growth ground to a halt in the first quarter.
IHS' Archer said France's PMI reading was "particularly disappointing and worrying".
"This reinforces concerns over the underlying state of the French economy and suggests that it is struggling markedly for growth after GDP (gross domestic product) was only flat in the first quarter," he added.
The PMI data is the latest sign that the region's recovery may be slowing. Two closely watched economic indicators—Markit's composite PMI (which includes both the manufacturing and services sectors) and the European Commission's Economic Sentiment Indicator—weakened in June.
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The final composite figure—or any revision to the flash estimate released last month—is set for release later this week. It comes after the euro zone's economy grew by just 0.2 percent in the first three months of the year, quarter-on-quarter.
Archer said euro zone GDP was like to have edged up in the second quarter, growing at around 0.3 percent on the quarter, but "it is evident that the euro zone is currently clearly finding it hard to build appreciable growth momentum".