Police Chief Arthur Smith said animals, including dogs, are deemed vicious and dangerous if they bite a human or another animal without provocation.
The animal's owner would be given 10 days to appeal after Washington County animal-control agents issue notice that the animal has been deemed vicious and dangerous, he said.
Smith said 15 dogs in the county fit that description.
Pet owners who violate the ordinance would face up to 90 days in jail and a $500 fine, according to the ordinance.
Councilwoman Kelly S. Cromer cast the lone vote against introducing the amendment.
Cromer said after the meeting that she needed more information before she could support changing the law.
"I may vote 'yes' next time," she said.
Councilman Lewis C. Metzner said the amendment made sense.
"The question is, 'Do you want a dog like that living in the City of Hagerstown?'" he said.
The ordinance does not specify animal breeds.
Last week, the council discussed giving the owner of a vicious and dangerous animal 90 days to remove it from the city.
That idea was scrapped, however, after Smith told the council that a dog, shortly after it was labeled vicious and dangerous, attacked a man and killed that man's dog in the city's West End.
