A similar restriction exists on SE for the comment field. I think it is a high quality solution to your problem and it also aligns with some of the design decisions you've already made.
"Sure, we can inform the user by placing the restriction below the field name."
The field hint describing the character length restriction —"enter at least 15 characters"— is set under the text-box.
"... we have decided do disable the button until at least 100 characters have been typed."
Although The button isn't styled as a disabled control, the user cannot submit a comment until she meets the minimum character length.
While 'disabled', the button is given a secondary function i.e. to highlight the restriction. When the user clicks the button, the restriction flashes, drawing the user's attention and ensuring the user reads the text.
The restriction also updates as the user types letting her know when she has met the minimum character length.
I think this updating hint could be improved by including characters after the number. If it's the first time the user is seeing the hint, it may take a moment for her to understand what the number represents.