An undercover agent with the Federal Bureau of Investigation who played a central role in an investigation of alleged corruption in men’s college basketball has been accused of misappropriating government money and spending it on gambling, food and beverages during the probe, people familiar with the matter said.

The Justice Department launched a criminal investigation last year into the agent’s alleged behavior, two of the people said. If he is found culpable, it could compromise his ability to participate as a witness at...