WASHINGTON—Transportation Secretary Elaine Chao has sold her shares in a paving-materials supplier after a Wall Street Journal report that she hadn’t fulfilled a pledge to relinquish the shares, agency documents show.

Ms. Chao, who is married to Senate Majority Leader Mitch McConnell (R., Ky.), sold her shares in Vulcan Materials Co. on June 3, according to documents submitted to the Office of Government Ethics.

On...