A federal judge in Texas Aug. 31 shot down an Obama-era rule that would have made some 4 million workers newly eligible for overtime pay but drew sharp criticism from business groups.

The Labor Department exceeded its authority by issuing the rule, which would have doubled—to $47,000 per year—the salary under which workers are automatically entitled to overtime pay for all hours beyond 40 a week, Judge Amos Mazzant said. The DOL focused too heavily on the amount of money...