Yes, it is permissible and even recommended to wear a face mask during Hajj, especially in situations where there is a risk of spreading or contracting contagious illnesses. Wearing a face mask is considered a precautionary measure to protect oneself and others from the transmission of diseases, including respiratory infections. It is in line with the Islamic principle of preserving and safeguarding one's health and the well-being of the community.
During Hajj, where millions of pilgrims from different parts of the world gather in close proximity, there is a higher risk of communicable diseases. Wearing a face mask helps to minimize the spread of respiratory droplets and reduces the risk of respiratory infections, including respiratory tract infections and viral illnesses.