MEXICO CITY—The surprise nomination Wednesday of a little-known economist as the next head of Mexico’s central bank raised concerns about whether the bank would be able to retain its independence under President Andrés Manuel López Obrador as the country struggles with rising inflation.

Mr. López Obrador, a leftist nationalist, nominated Deputy Finance Minister Victoria Rodríguez as the next governor of the Bank of Mexico, sparking a sharp depreciation of the peso. Investors and analysts expressed concerns about whether she was sufficiently qualified for the post.