The Bank of Japan
The MoF's power even extends to the central bank - the Bank of Japan. Although the governor of the Bank of Japan is appointed by the Cabinet, the MoF still has sway over the Bank because many BoJ directors and auditors are appointed by the Finance Ministry.
Despite this, the bank is fairly free of political tampering, and it has done a good job of controlling inflation over the last 15 years.
The Bank of Japan is modeled after the Federal Reserve System of the United States. The BoJ is a corporation, and it is consistently one of the most profitable firms in Japan.
Because Japan is much more dependent on bank lending than America, the BoJ controls the money supply mostly through the discount rate and reserve requirements.
Unlike the Fed, the BoJ really cannot use open market operations. This is because of Japan's small money markets, and because the Ministry of Finance wants to limit the number of short-term Japanese treasury bills.