The abrupt decision came after the desperate lobbying by the White House and its allies in Congress failed to mobilise adequate support to push the bill through, landing the first legislative blow to President Donald Trump.
Earlier, the president suffered the setback in travel ban executive order from seven Muslim countries which the federal judges blocked.
On Friday, the Republican leaders had planned a vote on the measure after Trump cut off negotiations with Republicans who had baulked at the plan and issued an ultimatum to vote - win or lose.
Trump told the Washington Post: "We just pulled it."
Amid a chaotic scramble for votes, House of Representatives Speaker Paul Ryan, who has championed the bill, met with Trump at the White House before the bill was pulled from the House floor after hours of debate.
Trump told the Post the healthcare bill would not be coming up again shortly and that he wanted to see if Democrats who uniformly objected to the Republican plan would come to him to work on health care legislation, a Washington Post reporter said on MSNBC.
Without the bill's passage in Congress, former Democratic President Barack Obama's signature domestic policy achievement, the 2010 Affordable Care Act - known as Obamacare - would remain in place despite seven years of Republican promises to dismantle it.
Repealing and replacing Obamacare was a top campaign promise by Trump in the 2016 presidential election, as well as by most Republican candidates, "from dog-catcher on up," as White House spokesman Sean Spicer put it during a briefing on Friday.
The House failure to pass the measure called into question Trump's ability to get other key parts of his agenda, including tax cuts and a boost in infrastructure spending, through a Congress controlled by his own party.
Trump already has been stymied by federal courts that blocked his executive actions barring entry into the United States of people from several Muslim-majority nations. Some Republicans worry a defeat on the healthcare legislation could cripple his presidency just two months after the wealthy New York real estate mogul took office.
In a blow to the bill's prospects, House Appropriations Committee Chairman Rodney Frelinghuysen announced his opposition, expressing concern about reductions in coverage under the Medicaid insurance program for the poor and the retraction of "essential" health benefits that insurers must cover.
"We need to get this right for all Americans," Frelinghuysen said.