Minnesota law specifically provides that Marriages may be solemnized among Hindus or Muslims by the person chosen by a local Hindu or Muslim association, according to the form and usage of their respective religions. Minn. Stat. §517.18.
Minnesota will recognize marriages that are solemnized in another country so long as the marriage was considered valid and appropriately solemnized in the other country. As an example, if you were married in India, moved to Minnesota and now wish to get a divorce, you do not need to prove that your marriage in India was valid so long as the marriage was considered valid in India at the time that it was solemnized.