Maryhill Housing Association has won a court victory over the tenant, who refused repeated demands to register one dog and then brought a second one into the property.
The owner has been given 14 days to remove the animals from the apartment at the 20-storey Glenavon flats in Maryhill.
Housing chiefs are phasing out the ownership of dogs in multi-storey properties.
Tenants who already have a dog must register the animal and agree not to get another one if the pet dies.
However, the association said it had "no option" but to go to court after one tenant refused to comply.
A sheriff has now banned the tenant from keeping dogs, ordered the animals removal from the home and issued an interdict which prevents the female from having any more dogs.
The ruling - granted at Glasgow Sheriff Court - means the tenant has 14 days to remove the dogs from the property.
It is believed to be the first time a housing association in Glasgow - and possibly beyond - has taken legal action to enforce one of its policies in relation to animals.
Maryhill Housing Association said the tenant was the only one of around 15 dog owners in the flats who failed to comply with the registration process.
Housing associations and Scottish councils have their own policies on dog ownership in multi-storey properties.
Some, including Glasgow Housing Association, include in the tenancy agreement that residents must agree not to keep a dog.
However, the policy is not generally enforced if owners are responsible.
In a second victory for Maryhill HA, another tenant has been banned from keeping dogs in a tenement flat, following complaints from neighbours.
The association said it was forced to act after a number of complaints about a tenant who had more than one dog and was visited regularly by family members who also have dogs.
This tenant has also been banned by the sheriff from keeping dogs in the property, must remove them and is also prevented from allowing dogs to visit the property.
Willy Briody, Chief Executive of MHA, said: "It is extremely unusual for us to take legal action of any kind against a tenant but in both situations we felt we had simply no option. Legal action is always a last resort.
"The Glenavon tenant had defied us on our dogs policy, which required the animal to be registered.
"The owner then obtained a second dog which was also in breach of our policy.
"Attempts to engage with this tenant failed and it was decided to go down the route of seeking a judicial ruling, which we are very pleased to have obtained.
"Maryhill Housing Association does promote responsible dog ownership but at all times we must consider the wellbeing and needs of other tenants living nearby.
"In the case of the second tenant there was no doubt that the number of dogs in this property was entirely unacceptable and were the subject of a number of repeated complaints.
"The association will continue to rigorously enforce our policy in relation to dogs."
The association stressed it was not opposed to tenants in other properties having dogs and offers a free micro- chipping policy.
Edinburgh City Council has a policy restricting dog ownership in tower blocks but the policy is not rigidly enforced.
Housing chiefs say taking legal action to enforce a prohibitive tenancy condition, including the clause on not keeping dogs within multi-storey blocks, is difficult and can be a lengthy legal process.