The analysis, conducted by researchers at the Rand Corp., was based on proposals made by both campaigns this year.
Clinton's plan calls for building on and tweaking President Barack Obama's Affordable Care Act. Trump wants to gut that law, known as Obamacare, and replace it with a tax deduction that would allow people with individual insurance coverage to deduct the cost of their premiums from their taxes, as well as several other measures.
The report found that GOP nominee's health proposals are apt to have a much more dramatic effect — as well as an opposite one — on the nation's uninsured rate than Clinton's. At the same time, the real estate mogul's health-care package would cost the federal government less money than Clinton's, according to the analysis.
If Trump wins the White House and most of his health plan becomes law, 25.1 million people would lose their insurance by 2018 as a result of both a full repeal of the ACA, and a move to award Medicaid funding in block grants to states, the analysis found.
That number is about 5 million people more than the number who have gained coverage as a result of the ACA since 2010.
Even on the low end, the report found, Trump's proposals would significantly increase the number of uninsured.
About 15.6 million people would lose coverage even if Trump only succeeds in repealing the ACA and implementing a tax deduction for people who purchase health insurance, according to the analysis. Just repealing Obamacare and implementing no other Trump health-care proposal would eliminate insurance for nearly 20 million people, it said.
Despite increasing the total number of uninsured people, two Trump policies could actually boost the number of higher-income people with health insurance, according to the report.
About 2.7 million such people, defined as members of families of four earning more than $60,750 annually, would gain coverage if Trump's insurance tax deduction were adopted. And 1.4 million such people would gain coverage if his proposal to allow insurance sales across state lines were adopted, researchers found.
At the same time, Trump's proposal would increase out-of-pocket costs for customers on the individual insurance market by $300 to $2,500 above the current average of $3,200.
The researchers said the fewest number of people who would gain coverage under Clinton's plan would be 400,000 by 2018. That would be the case if just her proposal to allow a government-backed insurance plan on Obamacare marketplaces became law.
The analysis also found that Clinton's proposals would tend to help low- and moderate-income people the most in reducing their out-of-pocket health-care costs by an average of 33 percent.
At the same time the Commonwealth Fund released the analysis, it also unveiled an online tool that allows people to compare Trump's and Clinton's health-care proposals, and to see the impact each plan would have on the uninsured rate, the deficit and out-of-pocket costs.
The Trump campaign rejected the analysis by the fund and Rand as fiction.
"The RAND study models an imaginary plan they invented, but not anything resembling the Trump plan," Trump campaign deputy communications director Jessica Ditto said in an email to CNBC. "Our health care team in fact never spoke with anyone at either RAND or Commonwealth. We asked them to delay their report until they spoke with our health care team, but they declined to do so — preferring to continue based on incorrect information."
She added: "Their ludicrous claim that 20 million now covered would lose their coverage following a repeal is immediately disproven by the fact that any replacement we would adopt would ensure that those now receiving 'premium support' would be given subsidies or other forms of support to purchase health insurance in the private market through Health Savings Accounts. That single fact alone renders the report null and void."
Clinton campaign senior policy advisor Jacob Leibenluft said: "Hillary Clinton will build on the health-care progress we've made by expanding coverage to millions of Americans who need it and addressing the costs that families face."
"On the other hand, Donald Trump's proposals would strip coverage away from many more people, including low-income families and those who are already struggling with health problems," Leibenluft said.
"That said, there were clearly some faulty assumptions made in this analysis that over-inflated the cost of the plan. Other independent estimates have set the cost vastly lower."