If the couple has participated in a civil marriage, the MUN requires them to be divorced in both Islamic and civil procedures. Civil divorce cannot replace Islamic divorce, in the same way that civil marriage does not replace an Islamic Nikah. Marriage in Islam is considered to be a civil contract with a strong religious element. The Prophet  said in his last sermon during Hajj:
"Be careful how you treat women. You have accepted them by the Word of Allah, and you have established lawful sexual relations with them by the Word of Allah."