The relevant clause reads:
No Senator or Representative shall, during the time for which he was elected, be appointed to any civil office under the authority of the United States, which shall have been created, or the emoluments whereof shall have been increased during such time: and no person holding any office under the United States, shall be a member of either House during his continuance in office.
The SecState's salary was increased while Hillary was in the Senate, therefore it appears she is not eligible to serve as Secretary, at least not until after her Senate term expires. Now, there is a precedent for evading this clause; see the linked article for the "Saxby fix." And, of course, there is a chance that everyone will simply ignore the problem. Still, this will be interesting to watch during her confirmation hearing, assuming she is in fact appointed.