The letter also tells owners to "please continue to meet your legal obligations to avoid legal repercussions".
The letters, distributed on April 6, have confused and infuriated owners, including Bull Breed Rescue.
The rescue organisation posted on social media it would take the council head-on.
"Up until today, I have always had great pride at how well Christchurch City Council have dealt with dog and especially BSL related issues. Now I am just angry. Actually shaking as I type this angry," the group wrote on Facebook.
"The CCC has now decided to enforce that all menacing dogs are to be muzzled, ALL THE TIME, unless caged. That's in your home, while chasing the ball in the backyard, while snuggled up in bed with you. ALL. THE TIME!!!
"Game on CCC, animal welfare lawyers work for free. Yours will cost you a packet. We will fight this every step of the way and we have a small but very loud army behind us.
"Remember our dogs are not 'menacing' because they did anything wrong, they are menacing because they were born looking a certain way."
According to the council website, a dog is "menacing" if that dog either wholly or predominantly belongs the brazilian fila, dogo argentino, japanese tosa, american pit bull or perro de presa canario breeds or types.
The Bull Breed organisation, as well as dog owners, have accused the council of "redefining" the term 'at large' to mean any time that a dog is not caged - including in at its own home. The council's website, does not mention requiring menacing dog owners to muzzle their dogs in their own private homes, which has led to confusion for owners.
Dog owners saying the requirements are cruel, and break New Zealand's own animal welfare laws.
"F**king unbelievable. Muzzling a dog full time is torture for the animal, the stress and other detrimental effects would only hinder the dog's natural behaviour most likely changing the personality of the dog for the worst," one dog owner said.
Up until today, I have always had great pride at how well Christchurch City Council have delt with dog and especially...
Posted by Christchurch Bull Breed Rescue on Sunday, 8 April 2018
"So the way I read it is they are 'requiring' the breeds to be muzzled on private property. THAT would indicate that it's not legislation yet and unenforceable," another wrote.
Another furious dog owner added: "Like hell you can tell people what to do in their own home with their own dog. Understandable in a public place but on your own premises? Shove off."
The organisation is meeting animal welfare lawyers this morning.
The Christchurch City Council has been approached for comment.