MELBOURNE, Australia—Australian law-enforcement and intelligence agencies are scrutinizing the activities of one of Chinese President Xi Jinping’s cousins as part of broad probes of organized crime, money laundering and alleged Chinese influence-peddling, according to Australian officials.

Among other things, police are looking into the alleged 2017 use by the cousin, Ming Chai, now a 61-year-old Australian citizen, of what they describe as a money-laundering front company that has helped gamblers and suspected mobsters move...