A crack is forming in an emerging-market revival that channeled almost $60 billion into assets of developing economies during the first months of 2017.

While money is still flowing in, some investors, such as investment manager Neuberger Berman, UBS Wealth Management and the hedge fund CCTrack Solutions, have been cutting back on emerging-market bets. The currencies of South Africa, Brazil, Poland and Turkey are down from their first-quarter peaks. And though the Russian ruble has had a good run, the iShares MSCI Russia Capped...