The Federal Reserve has designated Deutsche Bank AG’s sprawling U.S. business as being in a “troubled condition,” a rare censure for a major financial institution that has contributed to constraints on its operations, according to people familiar with the matter.

The Fed’s downgrade, which took place about a year ago, is secret and hadn’t previously been made public. The “troubled condition” status—one of the lowest designations employed by the Fed—has influenced the bank’s moves to reduce risk-taking in areas including trading...