By the time they arrived, a bystander may have killed the small shark, according to the Palm Beach Post.
Ocean Rescue Captain Clint Tracy told the Sun-Sentinel that medical personnel used a splint board to hold the woman's arm and the shark was put on the stretcher with her to take her to the hospital.
"I have never seen anything like it," Tracy told the newspaper. "Never even heard of anything like this."
The woman was listed in stable condition.
Tracy, the Ocean Rescue captain, told the Sun-Sentinel that some swimmers had been antagonising the small shark, though he did not know whether the woman played a part in it.
An 11-year-old told the paper that people had been "messing with it" - holding the shark up by its tail.
Nurse sharks - known as easy-going creatures - are considered the "couch potatoes" of the shark world, according to the National Park Service.
The creatures are recognised by their small size - they typically measure about 0.3m in length when they are born and can grow to 2m - and their razor-sharp teeth, according to the National Park Service:
Knowingly or not, people swim near nurse sharks every day without incident. Attacks on humans are rare but not unknown, and a clamping bite typically results from a diver or fisherman antagonising the shark with hook, spear, net, or hand.
The bite reflex is such that it may be some minutes before a quietly re-immersed nurse shark will relax and release its tormenter. The small teeth seldom penetrate deeply but are razor sharp. Holding still reduces damage to both shark and man. Leaving sharks alone is the best tactic.
ABOUT SHARK ATTACKS
1 There were 98 unprovoked shark attacks around the world in 2015, which topped the previous record of 88 attacks in 2000, according to the International Shark Attack File.
2 More than half of the attacks last year occurred in the United States, and most of those attacks took place around Florida.
3 Last year, three out of 10 shark attacks worldwide took place in Florida. Florida saw 30 bites last year, which was higher than the year before (23) but still shy of the record set in the state (37 attacks in 2000).
Jim Abernathy, a local shark expert who gives dive tours along the coast, told ABC affiliate WPBF that he believes the nurse shark was fighting back when it bit the woman on Monday.
"I'm 99 per cent sure that the person grabbed on its tail, and because the shark is only that big, it turned around and bit her right on the arm," he told the news station, adding: "The sad thing about all of this is the shark was minding its own business, got taken to a hospital [and] will be killed because someone pulled its tail."