Stock indexes that rode accelerating global growth to fresh records in January are now hamstrung by a moderate but unmistakable slowdown in economic momentum in Europe and elsewhere.

Business activity globally has slowed from multi-year highs, according to the JPMorgan Chase and IHS Markit global purchasing managers index. The global manufacturing index fell to 53.1 in May, a nine-month low. The services index for April, which will be updated for May on Tuesday, slid to 53.8 from 54.8 two months earlier. And business activity...