Federal prosecutors in New York are investigating USA Swimming, including allegations that the organization stifled athlete sexual-abuse claims, concealed its assets and improperly reaped hundreds of thousands of dollars in rebates from its in-house insurance company, people familiar with the matter said.

Over the past year, a federal grand jury in Manhattan has heard evidence in the investigation, which is being led by the Manhattan U.S. Attorney’s Office and the Federal Bureau of Investigation.

Agents...