That's the topic of this article by law prof Nathan Cortez. Here's the abstract:
The Federal Food, Drug, and Cosmetic Act (FDCA) does not expressly prohibit companies from marketing or promoting drugs for unapproved, "off-label" uses. The FDA itself acknowledges that off-label promotion is not a "prohibited act" under the statute, or an element of any such act. Instead, the FDA uses off-label promotion as evidence of other statutory violations. This Article engages in perhaps the most thorough statutory construction analysis of the FDCA on this question, finding that the statute does support the FDA's functional ban on off-label promotion. Using various tools of construction, I find that several sections of the FDCA assume or expressly contemplate a ban on off-label promotion, and that the FDCA's regulation of medical products, as a whole, depends on such a ban.