The association said its monthly manufacturing index fell to its lowest level since January, down to 50.5 from 56.2 in June. Analysts had predicted a drop to 55.1.
A reading above 50 suggests growth in the sector, which makes up about one-sixth of the economy.
Factories boosted production earlier this year to meet rising demand after a rise in retail sales. However, it did not lead to new hiring or stronger investments in the business sector, which the Federal Reserve has said are key to sustainable future economic growth.