• The CDC's new mask guidance provides "a pretty strong incentive" for Americans to get the Covid shot, Dr. Scott Gottlieb told CNBC on Friday.
• "I wouldn't be surprised if we see a bump up in the number of people going out to get vaccinated because now, being vaccinated provides more value," the former FDA chief said.

The CDC's updated face mask guidance is likely to prompt vaccine-hesitant Americans to get a Covid shot, Dr. Scott Gottlieb told CNBC on Friday.

"This is going to provide a pretty strong incentive for a lot people who might've been on the fence about getting vaccinated to go out and get vaccinated," the former U.S. Food and Drug Administration commissioner said on "Squawk Box."

In most indoor and outdoor settings now, fully vaccinated people do not need to wear a face covering or keep 6 feet of social distance from other individuals, the Centers for Disease Control and Prevention said Thursday. Masks still need to be worn at businesses that require them, the CDC said, as well as on airplanes and public transportation.

Nevertheless, the public health agency's relaxed stance is a major development in America's efforts to fight the coronavirus. It comes as 36% of the U.S. population has been fully vaccinated against Covid, per CDC data. About 47% of Americans have received at least one Covid vaccine dose.

The pace of new vaccinations has slowed in recent weeks, prompting government officials to look for ways to encourage more Americans to sign up for a Covid shot. That includes efforts to build trust in the vaccine, expand availability into harder-to-reach communities and create incentives. In Ohio, for example, Gov. Mike DeWine unveiled a plan to give $1 million to five of the state's residents via a lottery; the recipient must be vaccinated in order to be eligible for the prize.

The eased guidance from the CDC might be enough on its own to spur an uptick in vaccinations, according to Gottlieb, who led the FDA from 2017 to 2019 in the Trump administration. He now serves on the board of vaccine maker Pfizer.

"I wouldn't be surprised if we see a bump up in the number of people going out to get vaccinated because now, being vaccinated provides more value. You can go around in a mask in an honest fashion," he said.

Gottlieb acknowledged the concerns shared by some public health experts who believe unvaccinated people will use the new CDC guidance as cover to forgo a mask in businesses. However, he said, "I think people who will do that, would've done it anyway."

In general, Gottlieb said the CDC's mask decision is the right one now that the country has seen sustained declines in new coronavirus infections and a significant share of the population has been vaccinated, offering protection against severe disease and death.

He pointed specifically to the high vaccination rates among older Americans, who have an elevated risk of dying from Covid. Nearly 72% of Americas aged 65 and up have been fully vaccinated.

"I think the worst thing you could say about the action that the CDC took is, 'Well, maybe they could've waited another week,'" Gottlieb said. "At some point, we're going to have to move past coronavirus and start living normally again," he added. "We're at that point right now. We're right at the cusp of being able to take masks off and start reengaging in normal activities."

Dr. Ashish Jha, dean of Brown University's School of Public Health, told CNBC on Thursday that the new mask guidance is "really terrific news" for fully vaccinated people. However, Jha said he believes states should keep their indoor mask mandates in place for one more month. That would allow people who got their first Covid shot on April 19 — the day all U.S. residents aged 18 and up became eligible — to become fully vaccinated, he said.

Disclosure: Scott Gottlieb is a CNBC contributor and is a member of the boards of Pfizer, genetic testing start-up Tempus, health-care tech company Aetion and biotech company Illumina. He also serves as co-chair of Norwegian Cruise Line Holdings' and Royal Caribbean's "Healthy Sail Panel."