Kara McCullough, a scientist at the US Nuclear Regulatory Commission, appeared to link healthcare to employment.
But the beauty queen, 25, faced a backlash on social media.
It comes as the Trump administration battles to overturn Obamacare, which aimed to extend insurance coverage to the 15% of Americans who lack it.
Earlier this month the lower chamber of the US Congress passed a new healthcare act that Democrats say will leave millions uninsured.
However, Republicans in the Senate have indicated they will cast it aside and write a new law.
Asked during Sunday's pageant in Las Vegas whether healthcare was a privilege or a right, Miss McCullough said: "I'm definitely going to say it's a privilege."
She added: "As a government employee, I'm granted healthcare and I see first hand that for one to have healthcare, you need to have jobs.
"We need to continue to cultivate this environment that we're given the opportunity to have healthcare as well as jobs to all American citizens worldwide."
Her remarks divided liberal-minded and conservative-minded viewers. Some were quick to criticise her stance.
Miss McCullough - who was born in Italy and was representing Washington DC - was also asked if she considered herself to be a feminist but said she preferred the term "equalism" and said men and women had equal opportunity in US workplaces.
"I don't really want to consider myself - try not to consider myself like this die-hard, you know, like, 'Oh, I don't really care about men'," said the contestant, who says she wants to see more women employed in government science roles.
Some people on social media supported her views.
Obamacare has been opposed by Republicans since it was first proposed in 2009.
Republicans say the law imposes too many costs on business and describe it as a "job killer", although the number of jobs in the healthcare sector has risen since it was introduced.
Opponents have also decried it as an unwarranted intrusion into the affairs of private businesses and individuals.

The duo are the first Robins players to agree to join Guernsey FC since the clubs agreed a partnership deal earlier this week.
They are in Guernsey's squad for the trip to Herne Bay in Isthmian League Division One South.
If the pair play they will become the first non-Guernsey players to feature for the Green Lions.
"We're delighted to help Guernsey by sending Jake and Kodi to them for a month," Bristol City director of youth recruitment Brian Tinnion told the Guernsey FC website.
"This forms part of our plans for a bigger partnership with Guernsey. Working with their manager Tony Vance, we're looking to only extend this over time.
"We're already looking at the possibility of a pre-season friendly in Guernsey, potentially with the first team, or a Select XI including our under-23s."

The incidents, which occurred overnight between Sunday and Monday, took place in Granton, Boswall, Trinity and Hawthornvale.
The cars targeted all had their windows smashed or had attempts made to smash them.
About 25 incidents have been reported to police, however there may have been other vehicles damaged.
Due to the number of incidents and the scale of the damage, officers are treating the incidents as linked and are appealing for witnesses to come forward.
Insp Shane McKenna, of Drylaw Police Station, said: "This is an appalling number of vandalisms and the sheer scale of the damage caused is completely unacceptable.
"Not only has a lot of damage and inconvenience been caused to a large number of people, it has also caused a number of police resources in the north of Edinburgh to be diverted in order to investigate.
"We are eager to trace those responsible as soon as possible. We would ask that anyone who was in the north Edinburgh area on the evening of Sunday, November 13, and saw this damage take place, to get in touch with us at their earliest convenience."
The new Miss USA beauty pageant winner has sparked controversy by declaring that healthcare was a "privilege", not a right.
[NEXT_CONCEPT]
Guernsey FC have signed Bristol City forward Jake Andrews and defender Kodi Lyons-Foster on month-long youth loans.
[NEXT_CONCEPT]
Police in Edinburgh are investigating after 25 cars were vandalised in one night across the north of the city.