Mr Trump’s Twitter outburst has intensified a feud with the black congressman days before the national holiday honouring Martin Luther King.
Trump tweeted that Georgia Democrat Mr Lewis “should spend more time on fixing and helping his district, which is in horrible shape and falling apart (not to mention crime infested) rather than falsely complaining about the election results”.
The incoming president added: “All talk, talk, talk - no action or results. Sad!”
Mr Lewis, among the most revered leaders of the civil rights movement, had his skull fractured during the march in Selma, Alabama, more than 50 years ago and has since devoted his life to promoting equal rights for African-Americans.
The weekend clash highlighted the sharp contrast between how many African-Americans view Mr Trump’s inauguration compared with Barack Obama’s eight years ago.
It also demonstrated that no one is immune from scorn from a president-elect with little tolerance for public criticism.
Mr Trump has found political success even while attacking widely-lauded figures before and after the campaign - a prisoner of war, parents of a dead US soldier, a beauty queen - and now a civil rights icon.
Mr Lewis, a 16-term congressman, said on Friday that he would not attend Mr Trump’s swearing-in ceremony at the Capitol on January 20 - the first time he had skipped an inauguration since joining the US Congress 30 years ago.
“You know, I believe in forgiveness. I believe in trying to work with people. It will be hard,” he told NBC’s Meet The Press in an interview to be shown on Sunday.
“It’s going to be very difficult. I don’t see this president-elect as a legitimate president.”
Mr Lewis added: “I think the Russians participated in helping this man get elected. And they helped destroy the candidacy of Hillary Clinton.”
His spokeswoman, Brenda Jones, declined to respond to Mr Trump and said the Mr Lewis’ “opinion speaks for itself”.
“We as a nation do need to know whether a foreign government influenced our election,” she said.
US intelligence agencies have said that Russia, in a campaign ordered by President Vladimir Putin, meddled in the election to help Mr Trump win.
After spending weeks challenging that assessment, Mr Trump finally accepted that the Russians were behind the election-year hacking of Democrats.
But he also emphasised that “there was absolutely no effect on the outcome of the election including the fact that there was no tampering whatsoever with voting machines”.
Democrat Mrs Clinton received 2.9 million more votes than Mr Trump but lost the Electoral College vote.
Mr Lewis’ Democratic colleagues rushed to his defence on Saturday.
California’s Ted Lieu said he too would skip Mr Trump’s inauguration.
“For me, the personal decision not to attend the inauguration is quite simple: Do I stand with Donald Trump, or do I stand with John Lewis? I am standing with John Lewis,” he said.
The Democratic Party of Georgia called on Mr Trump to apologise to Mr Lewis and the people in his district.
“It is disheartening that Trump would rather sing the praises of Vladimir Putin than Georgia’s own living social justice legend and civil rights icon,” state party spokesman Michael Smith said.
But Mr Trump continued to jab Mr Lewis on Saturday night, saying that the congressman “should finally focus on the burning and crime infested inner-cities of the US”.
“I can use all the help I can get!” Mr Trump tweeted.