The headline index (the Purchasing Managers' Index) fell from 54.8 in April to 53.5 in May.
Manufacturing expanded for the 34th consecutive month, the institute said.
Numbers above 50 show growth and numbers below 50 indicate a contraction.
The institute said 13 of 18 manufacturing groups showed growth in May. The strongest growth was seen in apparel, non-metallic mineral products, furniture and related products, miscellaneous manufacturing, primary metals and electrical equipment.
Four industries -- plastics and rubber products, petroleum and coal products, food, beverage and tobacco products and transportation equipment -- reported contractions in May.
The component index for new orders rose from 58.2 to 60.1. The employment index showed growth, but at a slower pace, dropping from 57.3 to 56.9.
The prices index changed direction and turned negative, shifting from 61 to 47.5.