WASHINGTON—The number of Democratic lawmakers planning to skip Donald Trump’s inauguration ceremony Friday is growing, with more joining in the boycott after the president-elect took to Twitter over the weekend to rebuke civil-rights leader Rep. John Lewis (D., Ga.) for saying Mr. Trump wasn’t a “legitimate president.”

Minnesota Rep. Keith Ellison, who is running to become the next Democratic National Committee chairman, said on Monday he wouldn’t attend the inauguration, citing the war of words between Mr. Trump and Mr. Lewis...