Looks like a severe infestation of spider mites.
I'd isolate it far from your other plants as they are highly transmitted between plants.
They usually come from a lack of humidity where they quickly spread all over the plant and suck out its juices eventually killing it.
There are many methods such as insecticidal soap and neem oil but your infestation seems like it needs something more heavy duty.
I'll let someone else chime In on proper Control as im not to familiar with dealing with them in great numbers such as this!
If you notice any other webbing on you other plants I'd quickly spray then with water/dish soap mix and isolate then for a while. Google control methods for spider mites and you will find tones of recipes and control options.
Good luck with it

Thanks so much for the advice, MrBlurbs. I just relocated it and gave it a light spray in the shower. Half of the leaves dropped off, but I don't see any more cobwebs or spider mites. I'll continue misting it every day or two and keep an eye out for more mites.