No, a monk's fists are not considered weapons.
Monk's Martial Arts states
Your practice of martial arts gives you mastery of combat styles that
use unarmed strikes and monk weapons, which are shortswords and
any simple melee weapons that don't have the two-handed or heavy
which means that even for the monk, unarmed strikes are not weapons, and thus not valid targets for spells and effects which target weapons.
This is reinforced by the rules on melee attacks (Player's Handbook - Chapter 9 - Making an Attack - Melee Attacks - page 195)
Instead of using a weapon to make a melee weapon attack, you can use
an unarmed strike: a punch, kick, head-butt, or similar forceful blow
(none of which count as weapons).