Virginia Gov. Glenn Youngkin, a Republican, is facing heavy backlash for remarks about House Speaker Nancy Pelosi, D-Calif., less than a day after her husband was the victim of a brutal attack in their San Francisco home.

At a Virginia campaign rally for GOP congressional candidate Yesli Vega, Youngkin alluded to the Friday home invasion and subsequent attack, which left Paul Pelosi, 82, with a skull fracture and serious injuries to his right arm and hands.

“There’s no room for violence anywhere, but we’re going to send her back to be with him in California,” Youngkin said at the e...