Meanwhile, as many as 1 million Californians who buy individual policies are having their coverage discontinued despite President Barack Obama's promise that it wouldn't happen.
If healthy people avoid buying insurance on the exchanges, it will undermine insurers' business models and ultimately force premiums higher.
If those signing up trend to the elderly and sickly "your insurance is going to cost more and that will discourage those younger people from coming in," warned Lisa Folberg, a vice president with the California Medical Association. "There's still a lot of enrollment and outreach work that needs to be done."
Wednesday's Health and Human Services report provided the first glimpse into enrollment operations at Covered California, which faces a monumental task to reach millions of people without insurance and sway them to sign up under the federal Affordable Care Act.
The report, covering the start of open enrollment on Oct. 1 through Nov. 2, also showed that about 80,000 lower-income people would be eligible for expanded Medicaid coverage under another prong of the overhaul.
California counts nearly 7 million people without health coverage.
Agency officials described the first enrollment figures as encouraging, but Republican state Assemblyman Dan Logue, who represents a district north of Sacramento, predicted a troubled start.
"Covered California is giving you the best-case scenario, but where's it going to be 12 months from now?" he said. "I'm pretty sure it's going to be unsustainable."
The 35,000 figure was defined in the federal report as the number of people who have "selected" a plan through the insurance exchange. According to HHS, that means the number of people who have chosen a specific insurance plan, whether or not they have actually followed through and begun paying the premium for it.
Covered California said sign-ups have accelerated since then, to about 2,400 people a day so far this month.
The figures "show momentum and very high consumer interest," Peter Lee, the exchange's executive director, said in a statement.
Younger and healthier people who use fewer services are needed by insurance companies to balance the cost of treating those who are sicker and more expensive to cover.
In addition to the state-by-state numbers, the Health and Human Services report also provided the overall figure for national enrollment under President Barack Obama's national health reforms.
It said that fewer than 27,000 people managed to enroll for health insurance last month in the 36 states relying on the problem-filled federal website. States running their own websites, including California, did better than the federal government, together reporting more than 79,000 sign-ups.
Even so, total private insurance enrollment after the first month of the health care rollout was only about one-fifth what the administration had expected during that time period.
Enrollment numbers nationwide totaled 106,185. A Sept. 5 administration estimate had projected that 494,620 people would enroll in the first month.
During a Wednesday news conference, Lee said Covered California will have a breakdown of its enrollees next week.
The launch of the Affordable Care Act, also called "Obamacare," has been plagued by technical problems with the federal government's website. Several states that run their own exchanges, including Oregon and Hawaii, also have experienced significant technical setbacks that have prevented people from signing up.