Yes, but not as easily as humans.
I have had to get two tetanus shots in the last three years, thanks to a combination of rusty wire and a messy chicken coop. The last time it came up, it started me wondering: shouldn't we be vaccinating our animals against tetanus?
Unlike many other diseases which are caused by a species-specific viruses, tetanus is caused by the clostridium bacteria. When Clostridium tetani gets hold of a body, usually through a deep puncture wound, it produces a neurotoxin that causes the classic spasms and contractions that lead to the disease's colloquial name, "lockjaw."
It turns out that if I owned horses, I would probably already know the answer to my question. Horses and humans are both more vulnerable to tetanus than other animals. Horses frequently contract tetanus, often by stepping on a nail in the stall or barnyard. In fact, General Robert E. Lee's favorite horse Traveller died from tetanus contracted by stepping on a nail.
Incidentally, although the popular image of tetanus transmission is a "rusty nail," the rust has nothing to do with it. C. tetani flourishes in damp muddy conditions, particularly those contaminated by livestock. The same conditions that will cause a nail to turn rusty. However, you can get tetanus from a non-rusty nail, or from any other puncture wound.
Horses and humans both receive tetanus vaccinations on a regular basis. But what about dogs and cats? It turns out that cats are virtually immune to tetanus. However, dogs lie somewhere in the middle.
Dogs certainly do get tetanus. And interestingly, about 75 percent of the introducing wounds are from foxtail awns. These are the sharp, arrow-barbed seeds of the foxtail grass. Once stuck in a dog's coat or between its toes, the awn can work its way into the dog's body, causing a painful lesion - and introducing tetanus.
If the dog is treated quickly, it will often make a full recovery. The basic procedure is to provide supporting care: the dog may need to be put on a respirator to compensate for its paralyzed lungs, and the vet will probably put it under general sedation to relieve the painful muscular contractions and seizures.
However, dogs do not get tetanus often enough or easily enough to warrant receiving a regular vaccine. If a dog is injured in a way that could introduce tetanus (like stepping on a nail, getting a foxtail awn, a bite from another dog, etc) the vet will often give it a tetanus shot at the time of treatment, just to be on the safe side. Luckily, because it takes time for C. tetani to build up in the body, a vaccine is effective even after exposure, if it is caught soon enough.