It is not necessary; because a woman's foot is not considered 'awrah (nakedness) in prayer, as the covering is for the sake of avoiding temptation, which is absent during prayer. Moreover, religion alleviates hardship, and covering the feet in prayer involves hardship that is evident. Therefore, if a woman prays without covering her feet, her prayer is valid, but it is preferable to cover them, and she should also take care to cover her calves. Refer to: Al-Bahr Al-Ra'iq 1: 284.