Injured animal

Yes, plausible for your predator to be weakened over a few weeks.
A fight he lost w/ one of his own species or getting injured trying to take down prey could do it. Mebbe the deer got in some great kicks, fx the cat/wolf's spleen/kidney/liver enough to cause sig int hemorrhage/peritonitis...some extremely brave humans come along and restore him (after tranking the snot out of him).
I'd lean more to a cat than a wolf, as cats nearly always hunt alone and wolves do not, given their druthers.
And if you want the wound inflicted by a human, a gun shot wound makes sense. The person does not even have to have been hunting the predator, but took a stupid shot at a deer, missed and hit your predator who was stalking the deer a few hundred feet downrange.

Let's say your predator was a lone hunter, a big cat, etc. She tried to take down a large hooved animal and was kicked in the ribs hard enough to break some of them. She'd be unable to hunt and eventually starve to death. It might take longer than 3 weeks unless she was very hungry when the injury occurred.
I'm not sure why humans would want to intervene, but they could feed her and nurse her back to health if that's part of your story.

The graceful hunter recently took down somethig else and early into the meal, the cougar bit down visciously on the throat and ripped a chunk of flesh dripping dark blood all over the boardwalk. Gulping it down, she suddenly lost her aggressive posture. Her tail curled down between her legs as she tried to cough. Her tongue darted in and out of her maw, flicking like a angry squirrel's tail, trying to dislodge a piece of the chunk. Sometimes snorting and sometimes coughing, now she paced about and lay down ignoring her kill as the coyotes advanced circling in. But the cougar did not defend her dinner. She lay there preoccupied. The coyotes sorted out their share of the remains. They snarled and barked among themselves without regard to their main hunter who was now stretching her neck to and fro and flicking her tongue, trying to find any position to help. Blood dripped down the corners of her jowls, a sign of the danger. The dinner's hyoid bone had been bitten sharply from its attachments into a shape of a tailor made two pronged meat fork impaled into the soft tissue of her throat just behind the last teeth. She gagged and vommitted up the first few chunks that she had already swallowed. Unfortunately, this did not dislodge her fears. Half heartedly she growled and bared her teeth but the coyotes leaped in and out and grabbed her small fortune that should have been already in the bank. If she could not eat, she would die a slow painful death over several weeks. For hours she struggled with it, trying to get it to dislodge. The bone, impaled into the throat continued to promise that she would starve even with food in her mouth. Maybe she could catch and survive on mice? They might be able to bypass the entrapped hyoid bone and be swallowed. She could still breathe although not sneakily due to the coughing and gagging. It might take a few days of scraping with her tongue to tease off the soft tissue from the bone. At least that would probably stop the gagging. Hunting large game for now was out of the question. She will need to survive on water and maybe mice, however the hunger will slow her down. She will need to take advantage of any oppurtunity. In 2 weeks time, if she hasn't dislodged the bone at the back of her throat, then she might become prey herself.

Any wound causing infection would fit the bill. Also...

The Eskimos used to (perhaps still do in some areas) use a sharpened whale bone bent in half (it's flexible) and secured with twine and a bit of frozen whale blubber. Then they'd cut the twine and the blubber would be enough to hold it. Then they'd leave it out where wolves would find it. The wolf, like any dog, would swallow it whole. It thaws out in the stomach and pow, they eventually die from starvation/internal bleeding.