Yes, as in official DnD rules, unless it states otherwise in the wand's description, wands have a limited number of charges. According to the answer here,
Yes, wands have limited charges. One charge is used every time you use the wand (unless the item description says that it uses more charges). The number of charges can vary anywhere from 10-50.
BG1 does not show the number of charges left, so it is just guesswork to determine how many charges you have left. BG2...shows the number of charges if you have the wand in a quick-slot.
Sorcerous Sundries, an arcane shop in the city of Baldur's Gate, sells an unlimited quantity of all the wands in the game. So you don't need to be stingy with wand usage, since you can just buy more when they run out.
You can easily recharge wands by selling them and then immediately buying them back, or stealing them...
Obviously a shop that has infinite supply and sell/buy to recharge are both in violation of Official DnD rules, but they do exist in these games.
Also, while there is no direct way of checking the charges left in a wand in the first Baldur's Gate, you can infer how many charges are left in a wand by the amount that a wand will sell for.