What is the permissibility of a woman leaving the home for exercise if she observes proper modesty?
Thank you for your question. It is absolutely permissible for a woman to out for the reason that you described as long as she is doing it modestly.
Please see the details and explanations here:
May Allah give you the best of this world and the next.
[Ustadha] Shazia Ahmad
Checked and Approved by Shaykh Faraz Rabbani
Ustadha Shazia Ahmad lived in Damascus, Syria for two years where she studied aqidah, fiqh, tajweed, tafseer, and Arabic. She then attended the University of Texas at Austin, where she completed her Masters in Arabic. Afterward, she moved to Amman, Jordan where she studied fiqh, Arabic, and other sciences. She recently moved back to Mississauga, Canada, where she lives with her family.