It is really sad to hear that a wife or a husband commits such a sin. Faithfulness and loyalty should be the main characteristics of spouses. However, if such a thing happens, the wise and legal approach should be resorted to. The husband in question is not allowed to kill his wife; rather, he can resort to the court to have his legal rights, he can forgive her and give her a chance to reform her character, or he can divorce her.
The prominent Muslim scholar and Da`iyah, Zeinab Mostafa, states: A husband in this situation has to exercise patience and do nothing vile, he also has every right to divorce her.
In areas where Islamic Law is applied, he may do li`an (oath of condemnation). Due to the absence of four witnesses, he may swear before the judge that he saw her committing adultery and that Allah’s curse would be upon the liar, and she would also have the right to swear the same way.
After that the couple are separated and they cannot be husband and wife again. In the absence of li`an, the husband can simply divorce his wife if he found her in such a situation, and if he wants he has the right to take her to court as well.