House Speaker Mike Johnson announced that Rep. Matt Gaetz, who was tapped by President-elect Donald Trump to run the Justice Department, issued his resignation letter on Wednesday.

“I think out of deference to us, he issued his resignation letter effective immediately, of Congress,” Mr. Johnson said. “That caught us by surprise a little bit.”

He said that Mr. Gaetz told him “you can’t have too many absences” from the House, where Republicans are expected to have another narrow majority.

Mr. Gaetz is the third Republican whom Mr. Trump has scooped from the House, a move that whittles away at what is expected to be a thin majority.

Mr. Johnson, Louisiana Republican, said Florida law allows eight weeks to fill his seat, meaning that Florida Gov. Ron DeSantis could set a special election to replace Mr. Gaetz by Jan. 3, when Congress returns to kick off its new session.

The speaker said that he already contacted Mr. DeSantis, who is in Italy, to get the ball rolling.

Florida’s 1st Congressional District, which Mr. Gaetz represents, is deep red and Republicans will be confident of holding onto it.

The immediate resignation is also a bet by Mr. Gaetz on himself, as his nomination to be attorney general is expected to be the most controversial of Mr. Trump’s Cabinet picks.

Even in first hours since it was announced Wednesday afternoon, it was met by derision from fellow House Republicans and skepticism from some GOP senators who’d have to confirm him.

Regardless of whether Mr. Gaetz is confirmed by the Senate, his resignation will end an ongoing House ethics committee investigation into whether he engaged in sexual misconduct, accepted improper gifts, dispensed special privileges or engaged in illicit drug use.  

If confirmed by the Senate, Mr. Gaetz would lead the Justice Department that carried out a sex-trafficking investigation into him. After a two-year investigation, Justice Department prosecutors declined to charge Mr. Gaetz.

• Jeff Mordock contributed to this report.