There is absolutely no rule in the book that may prevent any kind of base class multiclassing (except special restrictions on races for certain classes or prestige classes, but they don't apply in this case).
It all boils down on how you roleplay level advancement. Some prefer the "videogame" approach where a level up is earned immediately, others instead play it as a long training that lasts weeks, if not months.
That said, your player should probably justify its choice, and explain why his warrior wants to become a Wizard. Maybe he picked up a few arcane tricks along his journey and now wants to deepen his knowledge on the matter, or he thinks that he absolutely has to learn magic for some reason.
You're also right that arcane magic requires a great amount of dedication, and you should probably wait to level him up untill he has enough time to study it and get that first level.
In the end, as I said, there is no rule about denying multiclass, but the standard multiclass penalities are the perfect fit for this situation. As he's already expert in swordfighting and thievery, having another thing to practice will need a greater effort, thus requiring more experience to level up again.
If the roleplay justification doesn't convince you, you could also veto it, as you're the master and you have the final word on everything, but I think this should be used as a last resort, only to prevent some kind of roleplay catastrophe.
A final (personal) thought, from DM to DM: your players want to have fun with their builds and characters, so denying them a choice just for a roleplaying quirk means denying him fun. His character is HIS character, and as a rule of thumb I always prefer not limiting players as much as I can (and this makes the game a balancing nightmare, but that's another problem).