These are the people of Israel as listed by their fathers' houses....
Numbers 2:32

By God's order, Israel was organized patriarchally and patrilineally. He chose fathers to lead worship, rule, command, survey, and judge.

There is no command in Torah against a woman in non-religious leadership, so I don't think it should be forbidden. However, God's nearly universal pattern is to appoint men whenever possible. The office of prophet is the only notable exception, but even then God chose men far more often than women.
#patriarchy