The U.S. is preparing measures ranging from criminal charges to sanctions against people it believes to be involved in Venezuela’s military-run emergency food program, according to U.S. officials, part of an effort to target what they describe as a large-scale money-laundering operation run by the government.

The measures are expected to be rolled out in the coming weeks and months as part of a bid to increase pressure on the Caracas regime. The U.S. and many other countries have recognized the political opposition as Venezuela’s...