WASHINGTON—The House Judiciary Committee said it would vote Wednesday on whether to hold Attorney General William Barr in contempt of Congress, escalating a dispute with the Trump administration after Mr. Barr missed lawmakers’ deadline to turn over an unredacted version of special counsel Robert Mueller’s report.

If the panel, chaired by Rep. Jerrold Nadler (D., N.Y.), approves the resolution, as expected, it would then need to be approved by the full House. The contempt measure refers Mr. Barr for possible federal criminal...