BNP Paribas SA will have a harder time managing Americans’ pension assets after the U.S. Labor Department exercised its rarely used power to prevent banks with a criminal taint from managing certain retirement assets.

The Department of Labor told the French lender in October that in the wake of a recent settlement with the Justice Department, the bank and affiliates would no longer be eligible for what’s known as a Qualified Professional Asset Manager exemption. Banks that are convicted of...