A computer glitch is preventing hundreds of mutual and exchange-traded funds from providing investors with the values of their holdings, complicating trading in some of the most widely held investments.

The problem, stemming from a breakdown early this week at Bank of New York Mellon Corp., the largest fund custodian in the world by assets, prompted emergency meetings Wednesday across the industry, people familiar with the situation said. Directors and executives at some fund sponsors scrambled to manually sort out pricing...