Markit's latest Purchasing Managers' Index fell to 53.6, from 54 in May, the lowest reading since October 2013.
Although any reading above 50 indicates expansion, analysts said the strong dollar was weighing on factory orders.
Meanwhile, the US Commerce Department said construction activity in May was its highest since late 2008.
Chris Williamson, chief economist at Markit, said in a statement that the PMI index pointed to a wider US economic slowdown.
"Purchasing managers are reporting the slowest rate of manufacturing expansion for over a year-and-a-half, suggesting that the economy is slowing again.
"The slowdown is largely linked to a third consecutive monthly fall in exports, in turn attributed by many companies to the strong dollar undermining international competitiveness," Mr Williamson said.
The weaker figure for June was despite the data's employment sub-index rising to 55.5 in June, up from 54.6 in May and the highest level since September 2014.
Meanwhile, US construction spending posted a solid gain in May, led by a big jump in non-residential projects.
The Commerce Department said spending rose by 0.8% from April, pushing total activity to a seasonally adjusted annual rate of $1.04 trillion, the highest level since October 2008.
All major categories showed increases in May, led by a 1.5% rise in non-residential building, which reflected increases in spending on hotels, manufacturing facilities and amusement parks, the Department said.
Developers said the spending on non-residential projects hailed positive news for the jobs market.
"It's fuelled by the feeling that the job growth is there, and tenants have need for more space because of new employees,'' said Richard Bezold, chairman of Akerman's real estate.

Thailand's Aphibarnrat, twice a winner this year, moved a shot ahead after a 40-foot breaking birdie putt at 14.
But Fitzpatrick, 21, who has led since day one as he seeks a first European title, picked up his fourth birdie at 15 to join the Thai at 12 under.
England's Luke Donald, now 66th in the world rankings, carded six birdies in nine holes in a 65 and is four adrift.
Another former world number one, Lee Westwood, is two shots further back after a 67, with 16 players within five strokes of the lead.
Donald, 37, who has not won since November 2013, said: "I've put myself in a good position. I'd love to shoot another round like this and if I did I think that might be good enough."
Welshman Bradley Dredge, seeking his first European Tour title since 2006, withdrew shortly before the start of the round because of a viral infection.
The 42-year-old, who lost his tour card in 2012 but regained it after finishing 81st on the Race to Dubai last year, had been only two shots off the lead.

Energy company BG Group said it was gradually taking workers from the Lomond installation - about 145 miles east of Aberdeen - by helicopter.
A Norwegian vessel which caught fire was about 12 miles away.
Tugs were being sent from Aberdeen to take the vessel under tow.

The 30-year-old joined City for £13.8m from Celta Vigo last summer and made 30 appearances, scoring six times.
Half of those goals came in his first three games. He did not start a league game - or score a goal - in 2017.
Last month he claimed his "daughter's face has changed colour" because of the English weather.
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He initially experienced racial abuse, but explains to BBC Sport's Nick Hope how he overcame that and after briefly considering representing France, is now targeting a medal at the 2016 Rio Olympics.
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US manufacturing growth eased in June despite jobs growth, but there was better news for the construction sector, according to two surveys.
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