A grand jury has issued a subpoena related to Manhattan federal prosecutors’ investigation into Rudy Giuliani, seeking documents from former Rep. Pete Sessions about his dealings with President Trump’s personal lawyer and associates, according to people familiar with the matter.

The subpoena seeks documents related to Mr. Giuliani’s business dealings with Ukraine and his involvement in efforts to oust the U.S. ambassador in Kyiv, as well as any interactions between Mr. Sessions, Mr. Giuliani and four men who were indicted...