Stop the Invasion Act This bill requires the President to bar the entry of certain non-U.S. nationals (aliens under federal law) into the United States if U.S. Customs and Border Protection (CBP) encounters a certain number of inadmissible non-U.S. nationals. Specifically, this bar shall apply if CBP detains or finds on average more than 30,000 such inadmissible individuals each month over the most recent 12-month period. The bar shall cease when the average drops below 30,000 encounters. Such encounters shall include non-U.S. nationals who seek entry into the United States when the President has suspended entry to prevent the spread of a communicable disease. While this bar is in effect, the President must prohibit the entry of non-U.S. nationals who are inadmissible for specified reasons related to illegal entry, violation of immigration law, or lack of documentation.