"Monthly heartworm" refers to a preventative medicine given to dogs on a monthly basis to protect them from a parasitic infection called heartworm disease, which can be life-threatening. Full definition
You will also keep the dog on monthly heart worm prevention. (powellpaws.org)
The adopter is expected to update the dog's vaccinations yearly, or as their vet recommends, and keep them on monthly heart worm preventative, also per their veterinarian's recommendation. (allearsbassetsanctuary.org)
Are your dogs given monthly heart worm prevention? (aavarescue.com)