Well, without magic you are limited to what classes?
Bard (Maybe. Without spells their Inspiration could really be a non-magical ability. They have expertise in skills and some of the subclasses get Extra Attack IIRC so they can fight reasonably well...)
Barbarian (Sure, just stay away from the magical-effect subclasses.)
Cleric (Nope.)
Druid (Nope.)
Fighter (No problem.)
Monk (Keep some of the subclasses out of the picture, but some are fine even in a no-magic setting.)
Paladin (No smites would be harsh, probably not going to work as is, so Nope).
Ranger (Sure, losing spells would suck, but they have some other features depending on the subclass that could make them work fine.)
Rogue (No problem.)
Sorcerer (Nope.)
Warlock (Nope.)
Wizard (Nope.)
So, the only no-go classes IMO would be most of the pure casters (Cleric, Druid, Sorcerer, Warlock, Wizard) and the Paladin.
I think the okay to of course classes would be Bard, Barbarian, Fighter, Monk, Ranger, and Rogue. Some subclasses won't work, but there are plenty that will IMO.
Otherwise, monsters would be different as well. I mean, a strict "no magic" can mean no dragons, etc. or just "no magic spells or items"--it depends on what you really mean by "no magic."