Although, there is no minimum GMAT score to apply to the Harvard Business School's two-year MBA program, data shows that their cut- off ranges from 680-770. The median score is 730 and in percentage is 80%. There are a few other criteria other than the GMAT score to get admission into HBS.

As you stated, your past academic and extra-curricular records have been quite up to the mark, displaying your personal qualities and potential. In addition, your work experience looks convincing. Professional experience carries significant weight-age and if presented wisely, it can take you further.

However, the gates to HBS are most likely to be closed for any GMAT score lower than 680. With your GMAT score at the lowest range of the cutoff, you might just narrowly escape admission to the program. Frame stellar essays. Try seeking professional help from admission consultants. You will have a better perspective and approach.

All the best!