Spanish police briefly detained prominent Kremlin critic Bill Browder in Madrid on Wednesday, acting on a request from Russia, highlighting Moscow’s attempts to cow its critics even when they are abroad.

Mr. Browder, a U.S.-born investor who has sharply criticized the Putin government, was arrested on what Spanish police and Mr. Browder said was a request from Russia. Spanish police soon released Mr. Browder because the appeal was no longer valid, said a spokesman for Spain’s national police.

The...