It’s just a little bit against the law…
Actually dogs are banned in Reykjavík. However anybody can get an exception. Banning dogs, but making exceptions for each dog makes the regulations quite strict. Which I, a dog owner (that’s Fífa in the picture), think is actually quite good.
The regulation basically says that every dog has to be registered to both an address and an individual. The individual can not have any animal abuse charges or criminal charges that suggest the dog will be used as a guard or attack dog. Actually several typical guard dog breeds are completely banned. All dogs have to be kept on a leash in Reykjavík, except in dogparks and owners have to clean up after the dogs.
If the owner breaks any of these rules, then the exception can be revoked. The neighbors also have a lot of power. If you live in an apartment and share an exit with other apartments, you must get a written approval from each and every one. If any neighbors complain about barking and such, then that weighs a lot.
Come to think of it, this is quite out of style with other things in Iceland. Generally rules are very flexible or nonexistent in Iceland. However these rules only apply in Reykjavík. There are probably similar rules in some towns as well.
One thing that surprises people though is how difficult it is to bring dogs or all animals actually to Iceland. If you bring animals to Iceland, they must be quarantined on a small island, Hrísey, for quite a long time (weeks generally). So don’t bring your pets with you on holiday to Iceland. These strict rules are because of Iceland’s isolation, many animals have little resistance to diseases around the world.