Yes Exercise can indeed be a cause of breast pain.
The breast pain during exercise usually happens because of friction so it's important to wear a good quality sports bra that can help prevent the friction caused during exercise so the breasts won't start hurting.
The underwire of your bra can also cause breast pain so if your breasts are hurting during exercise it's normal but you can prevent the breast pain while exercising by purchasing and wearing a quality sports bra while exercising.