The woman, who lives in a tenement owned by Mary-hill Housing Association, was served with the notice yesterday following a court order.
The housing association acted in response to complaints from neighbours about the tenant who is believed to have owned up to five dogs, including three Stafforshire bull terriers.
One of the dogs is said to have killed a neighbour's Yorkshire terrier.
The tenant, who lives in Fingal Street, has been banned by the sheriff from keeping dogs in the property and is also prevented from allowing dogs to visit the property.
Neighbours say the woman has been keeping the dogs at different addresses in an attempt to evade the authorities.
Neighbour Eileen Dempsey said: "The family allowed these dogs to roam the streets. On March 16 one of the bull terriers ran into the backyard of another house and killed a family's Yorkshire terrier.
"The same dog on March 25 came after my three-month-old puppy while my granddaughter was walking the pup up to my house.
"All people want is an assurance from the police that these dogs are gone."
Last week the Evening Times revealed how another Maryhill tenant had been banned from keeping dogs in a landmark court case.