Maryland would become the second state in the nation to ban the practice. New York banned it in 2019.
Supporters of the ban say declawing hurts the cat and leaves it unable to defend itself.
The Maryland measure bans declawing, unless it addresses a medical condition that compromises the health or well-being of a cat.
Veterinarians would not be able to declaw cats for cosmetic or aesthetic reasons, or for convenience in handling.
Veterinarians would face a fine of up to $5,000 for a first offense and up to $10,000 for a second offense, in addition to suspension or revocation of a license.
The bill also prohibits any person, other than a veterinary practitioner performing a declawing procedure.
The Maryland Senate passed a bill earlier in the legislative session. Each chamber would still need to approve the measure passed by the other to send the legislation to Gov. Larry Hogan.