The Arizona senator, who is battling brain cancer, said he "cannot in good conscience" vote for the new plan, which President Donald Trump backs.
Mr McCain said it was wrong to pass such far-reaching legislation without input from both main parties.
It is the second time he has thwarted his party leadership on the issue.
Republicans need 50 votes in a 100-seat chamber they control 52-48 to succeed. Democrats are united in opposition.
The Arizona senator's objection may doom conservatives' seven-year campaign to erase Democratic former President Barack Obama's signature legislative achievement.
In a statement on Friday, Mr McCain said such a bill demands extensive hearings, debate and amendment.
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