The list of Health Ministry recommendations carried by the Saudi Press Agency on Friday also advises the elderly, or those with chronic diseases, to postpone their pilgrimage.
The main pilgrimage season comes later this year but hundreds of thousands also visit the kingdom's holy sites during the month of Ramadan, which began this week.
Saudi Arabia announced two deaths on Sunday, bringing to 38 the number of deadly cases in the kingdom.
The new virus is related to SARS, which killed some 800 people in a global outbreak in 2003. It belongs to a family of viruses that most often cause the common cold.