While not quite what you had in mind, the closest I can think of is Lalia Clayhanger, wife of the Old Took's grandson Fortinbras II, who was sometimes referred to as "Lalia the Fat." Tolkien writes of her:
She was not at the famous Party (SY 1401), but was prevented from attending rather by her great size and immobility than by her age. [...] Lalia, in her last and fattest years, had the custom of being wheeled to the Great Door, to take the air on a fine morning.
The Letters of J.R.R. Tolkien 214: To A. C. Nunn (draft).
In the real world, obesity has been linked to (among other health effects) a wide array of foot disorders. If Lalia is so overweight that she is unable to move under her own power, it seems likely that she's done some serious damage to her feet and/or ankles.
However, I've not been able to find any reference to foot injuries caused by going barefoot through the countryside. As has been pointed out in comments1, Hobbits are described in the prologue as having tough soles, which would make these sorts of injuries much less likely:
[T]hey seldom wore shoes, since their feet had tough leathery soles
Fellowship of the Ring Prologue 1: "Concerning Hobbits"
SFF.SE's own Darth Melkor once pointed out that Hobbits were capable of wearing shoes (and that Bilbo was intended to have worn boots during the events of The Hobbit), which suggests those sorts of injuries are still possible, though they presumably don't make for very interesting reading.
Out of Universe
As revealed in some of the special features on the Lord of the Rings extended edition DVDs, at least two of the film hobbits received foot injuries on-set:
- Dominic Monaghan (Merry) got a splinter in his foot running down the bridge to Buckleberry ferry
- Sean Astin (Sam) cut his foot on a shard of glass in the Anduin, while filming the Parth Galen scenes
Presumably this is because, unlike their literary counterparts, film-Hobbits' feet only have latex soles, not leather.
1 By NKCampbell and Matt Gutting