Yes, there are quite a few exemptions

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You may qualify for an exemption if:

You’re uninsured for less than 3 months of the year
The lowest-priced coverage available to you would cost more than 8% of your household income
You don’t have to file a tax return because your income is too low (Learn about the filing limit.)
You’re a member of a federally recognized tribe or eligible for services through an Indian Health Services provider
You’re a member of a recognized health care sharing ministry
You’re a member of a recognized religious sect with religious objections to insurance, including Social Security and Medicare
You’re incarcerated, and not awaiting the disposition of charges against you
You’re not lawfully present in the U.S.

https://www.healthcare.gov/exemptions/