The U.S. Justice Department is pursuing a criminal investigation into whether Johnson & Johnson lied to the public about the possible cancer risks of its talcum powder, people with knowledge of the matter said.

The criminal probe, which hasn’t been reported previously, coincides with a regulatory investigation and civil claims by thousands of cancer patients that J&J’s Baby Powder talc was responsible for their illness. Now, a grand jury in Washington is examining documents related to what company officials knew about any carcinogens in their products, the people said.

Baby Powder accounts for only a tiny fraction of J&J’s annual...