Senate Majority Leader Mitch McConnell, who led the secret drafting of the measure and unveiled it last week, said lawmakers would continue negotiating, in a bid to bridge the "differences" that have split Republicans over the legislation.
"Consequently, we will not be on the bill this week. But we're still working toward getting at least 50 people in a comfortable place" to vote for the measure, McConnell said.
Senator David Perdue said earlier that he believed a vote would not occur this week as planned, but possibly "the first week when we get back" from the July 4 Independence Day recess.
The delay is a huge blow to Trump and Republicans who have spent the last seven years plotting an end to the Affordable Care Act, commonly known as Obamacare.
It also highlights the deep ideological divides within the party over how to improve the health care system while not cutting millions of Americans out of insurance coverage.