The major accreditation body (AACSB) requires that a minimum percentage of faculty are classified as a certain type of academic researcher which usually translates into having received a PhD from other accredited business schools and being actively involved in research. Thus, many schools list a business PhD from an AACSB school as a minimum job qualification and will not consider candidates without it.
I do not personally know any engineering PhDs who are tenured faculty in a management department, but I know a couple who have PhDs in IO Psych, Sociology, and Education/leadership.
I think that you will have a harder time getting a tenure track management position with an engineering PhD compared to a Business PhD. However, you could potentially overcome this if you have a very strong CV (A level pubs in mgmt journals).
That being said, A level journals are are not easy to publish in and management likely requires a different approach compared to engineering. I think it would be incredibly difficult to accomplish this as a PhD student.
Did you apply to any management programs? If you are committed to landing a position at a business school, it might be better to wait until the next application season.