Can the medical bills of someone injured on your property be covered by homeowners insurance?

They could be in some cases depending on how and why they were injured and what the relationship and residence status is to he named insured.

Your homeowners medical coverage is specific to the named insured(s). Generally this is the home owner and resident family members.

If someone else was injured on your property due to the insureds direct actions or through the insureds negligence for which you could be held liable then such an injury would be covered under the liability portion of your homeowners insurance policy.

Bear in mind though that a homeowner is not automatically liable for an injury on the property simply because you own it. The injury would first have to be demonstrated as the fault of the insured, otherwise the homeowner is not liable.