More than 60,000 employers will have to turn over worker pay data to the Equal Employment Opportunity Commission by Sept. 30, as part of an annual workforce data report known as the EEO-1.

A federal judge in Washington, D.C., set the deadline in an April 25 ruling from the bench. Proponents of the collection say it will help narrow systemic pay gaps based on race, sex, and ethnicity. Critics, however, say the collection will be burdensome for businesses—which altogether could...