The U.S. manufacturing sector shrank for the first time in three years last month, providing the latest sign that a global manufacturing pullback is weighing on the American economy amid rising trade tensions between Washington and Beijing.

Tuesday’s Institute for Supply Management’s manufacturing index, a widely watched gauge of factory activity, fell to 49.1 in August from 51.2 in the prior month. Readings above 50 indicate activity is expanding across the manufacturing sector, while those below 50 are a sign of contraction....