I thought this was an interesting observation. Ellacombe, speaking of the plants that do not occur in Shakespeare’s works, notes:
“Perhaps the most noteworthy plant omitted is Tobacco — Shakespeare must have been well acquainted with it, not only as every one in his day knew of it, but as a friend and companion of Ben Jonson, he must often have been in the company of smokers. Ben Johnson has frequent allusions to it, and almost all the sixteenth-century writers have something to say about it; but Shakespeare never names the herb, or alludes to it in any way whatever.”
What might account for this? On a level, the word itself does not seem Shakespearean (too exotic, non-European); on another level, Shakespeare’s plays don’t tend to treat of Shakespeare’s contemporary society; finally, I could see him disapproving of the practice; and finally finally, Shakespeare is unlike his peers in pretty much all respects, no reason for him to be similar in this one.
Here Wikipedia gives a rough idea of how widespread tobacco use was in Shakespeare’s England.
.i`` * ^ / . . . . . ` `~ 