Guide
Yes in many places — but three permissions, not one, decide it: the state, the landlord, and the local rulebook.
The question completes in search after search because the answer is genuinely three answers.
Licensing rules rarely require you to own the home. They require a home that passes inspection, where you live (for family child care), with the household's adults background-checked. Renters get licensed every day in every state.
Your lease is a contract, and most leases restrict business use or require written consent. Get the consent in writing, before you file — a licensing file built on a lease that forbids the business collapses at the first complaint, and "my landlord said it was fine" said aloud is not a document. Expect the landlord to ask about insurance; arrive with the liability policy quote in hand and the conversation changes.
Zoning decides whether a home occupation of this size is allowed at your address; many cities allow small family homes by right and require a use permit for large ones (California, for instance, treats small and large family child care homes as residential uses the city must allow, while leaving health-and-safety rules intact). HOAs are the private layer: some states void HOA bans on family day care, many do not. Both checks are address-specific, which is why the checker routes you to them as named local checks instead of pretending a state answer exists.
Every rule in this guide bends by state. Run your facts through the free checker and read your verdict with its citations.