Regarding the ruling on a man covering his face while in a state of ᾽Iḥrām:

Imam Ibn Qudāmah summarized the scholarly debate on this matter, saying:

“There are two opinions regarding a male pilgrim covering his face during ᾽Iḥrām:

The first opinion: It is permissible. This was reported from ῾Uthmān ibn ῾Affān, ῾Abd al-Raḥmān ibn ῾Awf, Zayd ibn Thābit, Ibn al-Zubayr, Sa῾d ibn Abī Waqqāṣ, Jābir, Al-Qāsim, Ṭāwūs, Al-Thawrī, and Al-Shāfi῾ī.

The second opinion: It is not permissible. This is the view of Abū Ḥanīfah and Mālik, based on the narration from Ibn ῾Abbās that a man fell from his mount and died. The Messenger of Allah (peace and blessings be upon him) said: ‘Wash him with water and sidr (lotus leaves), shroud him in his two garments, and do not cover his head or face, for he will be resurrected on the Day of Judgment reciting the Talbiyah.’ It is also argued that since it is forbidden for women to wear perfume in ᾽Iḥrām, the same rule should apply to men regarding covering the face. However, our opinion is based on the sayings of the Companions, and since no disagreement among them in their time is known, it is considered consensus.”

As for the ruling on a woman covering her face during ᾽Iḥrām:

A woman is prohibited from wearing a niqāb on her face or gloves on her hands. However, she is not prohibited from covering her face entirely with something that is not customarily considered a niqāb. This is based on a report from Abū Dāwūd narrated by ῾Āāishah (may Allāh be pleased with her), who said: “Caravans would pass by us while we were in ᾽Iḥrām with the Messenger of Allāh (peace and blessings be upon him). When they came close, one of us would lower her garment from her head over her face. When they passed, we would uncover our faces.”

A similar report is narrated from ᾽Asmā᾽ bint Abī Bakr (may Allāh be pleased with them both).

Based on that:

Wearing a face mask (like a medical or protective mask) should not be an issue for the pilgrim, whether male or female.

In addition to its medical and preventative benefits for both the wearer and those around them, it is not considered a typical face covering, nor is it worn by women as a form of niqāb. It is not the traditional niqāb that is prohibited in the texts. Similarly, if someone wears plastic bags or covers on their hands, they are not deemed to be wearing gloves, since plastic bags are not commonly classified as gloves.

No one who wears a face mask claims that they are muntaqib (veiled) according to linguistic or customary usage. The niqāb has a religious and customary distinct, recognized form both in Islamic and non-Islamic contexts.

Therefore, we see no objection at all to wearing a face mask for either men or women in ᾽Iḥrām—whether for illness or prevention—since it is not considered a form of clothing or a niqāb.

Fatwā issued by Dr. Khālid Naṣr