The Faculty of Arts and Sciences Committee said it was prohibiting "romantic or sexual relationships" regardless of whether a faculty member was teaching or supervising the student in question.
The ban applies to undergraduate and graduate students, and has been ushered in as part of a review of policy on sexual misconduct.
The review "determined that the existing language on relationships of unequal status did not explicitly reflect the faculty's expectations of what constituted an appropriate relationship."
It comes at a time when top American universities are on the defensive over complaints of sexual violence on campus.
Last May, the US department of education published a list of 55 colleges and universities under federal review for allegedly mishandling sexual assault and harassment complaints.
Harvard, in the northeastern US state of Massachusetts, was on the list. The university's historic rival, Yale, prohibited sexual relations between faculty and undergraduates in 2010.
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One of the few things that is considered just cause for losing tenure status in many Colleges.Universities - no big deal.