Masih Alinejad Harassment and Unlawful Targeting Act of 2021 or the Masih Alinejad HUNT Act of 2021 This bill imposes sanctions on foreign persons (i.e., individuals or entities) that are acting on behalf of Iran's government and involved in the harassment of certain individuals, such as human rights activists. The Department of State must periodically report to Congress the identities of foreign persons acting on behalf of Iran's government that are knowingly responsible for or complicit in the surveillance, harassment, imprisonment, or killing of citizens of Iran or the United States who seek to (1) expose corruption or illegal activity by Iranian government officials; (2) obtain, defend, or promote internationally recognized human rights; or (3) obtain, defend, or promote the rights and well-being of women, religious and ethnic minorities, and the LGBTQ community in Iran. The report must include foreign persons involved in such actions that occur inside or outside Iran. The President must impose property-blocking sanctions on persons identified in the report, as well as visa-blocking sanctions on the identified individuals. The Department of the Treasury must submit to Congress a report identifying any foreign financial institution that knowingly conducts a significant transaction with a person sanctioned under this bill. Treasury may prohibit the opening, or prohibit or impose strict conditions on the maintaining of a U.S. correspondent account or a payable-through account by such a financial institution.