First of all, it should be clear that Jumu`ah prayer is not obligatory for Muslim women, but if they do perform them, then they don’t have to perform Zuhr prayer.
In his well-known book, Fiqh As-Sunnah, the late Sheikh Sayyed Sabiq states: “Jumu`ah prayer is not obligatory upon women. There is no difference among Muslim scholars in this regard.
Tariq ibn Shihab reported that the Prophet (peace and blessings be upon him) said: “Jumu`ah prayer is a duty upon every Muslim in congregation, save four: a slave, a woman, a child, or a person who is ill.”
Should a woman pray Jumu`ah, it will be valid and she will no longer be obliged to pray the Zuhr. Women during the time of the Prophet (peace and blessings b upon him) attended the mosque and used to pray Jumu`ah with him.”
Dr. Muzammil H. Siddiqi, former President of the Islamic Society of North America, adds:
“It is correct that Jumu`ah prayer is not obligatory upon women, but women are allowed to pray Jumu`ah prayers in the mosque along with men. The Prophet (peace and blessings be upon him) said, “Do not prevent the female servants of Allah to come to the mosques of Allah.” (Reported by Al-Bukhari)
Women used to attend the Jumu`ah and other prayers in the Mosque of the Prophet (peace and blessings be upon him) during his lifetime. They were never told to pray Zuhr also. Thus, it is clear that if a woman prays Jumu`ah prayer in the mosque with the congregation, then this is sufficient for her. She does not have to pray Zuhr after that.”
Thus, though women are exempted from performing Jumu`ah prayer, they are allowed to perform it, and, in such a case, they need not pray Zuhr.