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The Scottish SPCA says there are currently no fixed rules about keeping pets in such accommodation and restrictions vary, but dogs are generally banned in most tower blocks.
But the charity’s “Pets and Tenants Together” campaign calls for those in council or social housing to be able to keep their pet.
The Scottish SPCA produced a manifesto for the Holyrood elections calling upon candidates to commit to developing an initiative which supports landlords and tenants to allow pets in homes.
It argues if people are not allowed to keep their pets it can be a devastating loss to both human and animal and can have a significant impact on people’s mental health and wellbeing.
A survey found 77 per cent of Scots believed housing associations and refuges should allow pets in order to keep animals and people together.
Scottish SPCA head of education, policy and research Gilly Mendes Ferreira said: “We don’t believe that someone should have to choose between a pet and a house.
“Many people without a home will have to make that impossible decision with some deciding to stay on the street over giving up a beloved pet.
“It has been proven that the human-animal bond has so many benefits on someone’s physical, mental and social health. Pets can help with loneliness and children growing up with pets have increased levels of physical activity.
“In the UK, it has been estimated that pet ownership saves the NHS £2.45billion each year due to the reduced number of visits to the doctor by people with pets.”
The charity says pets are relinquished for many reasons such as poverty, escaping abuse or changes in a person’s lifestyle, but often pets cannot be taken in to social or council housing by their owners due to restrictions on allowing pets in homes.
Ms Ferreira said: “We are asking for an initiative that will put pets and people first that provides all public and private landlords across Scotland with specialist advice and guidance on how to support pet friendly accommodation and access to incentives to help protect the human-animal bond."
The campaign was backed by Edinburgh Eastern SNP MSP Ash Denham, who said pets offered comfort, stability and companionship.
“Being forced to choose between your pet and a safe place to live is a choice no one should have to make.
"As MSP for Edinburgh Eastern I have been contacted by a number of constituents who have sadly been placed in this heart-breaking dilemma in the past.”
The Scottish SPCA says it wants to hear of people’s experiences of finding accommodation as a pet owner and is asking them to get in touch through its website or helpline.
Ms Denham said: "I would ask members of the public to visit the Scottish SPCA website to learn more about this campaign and if you have been affected by this to contact the charity directly with your personal experiences."