JEDDAH, Saudi Arabia—When Lina Mokhtar and her two sisters saw the news last month that Saudi Arabia would for the first time officially allow women to perform the hajj without a male guardian, the three of them immediately put in their applications.

On Saturday, Ms. Mokhtar and one of her sisters will be part of a limited group of some 60,000 worshipers to begin the pilgrimage—the second time the Covid pandemic has led Saudi authorities to cut the numbers of those permitted to perform the rite, a once-in-a-lifetime obligation for all Muslims able to physically and financially able to make the journey. In normal years more than two million pilgrims gather for the hajj.

Ms. Mokhtar was surprised by the move to do away with the requirement that women pilgrims need a mahram, a close male relative, to accompany them, but hailed the decision.

“It is kind of difficult depending on someone else or asking a mahram of yours, ‘Please let us go to hajj,’” said the Jeddah-based market researcher in her late 40s. “You can make that decision yourself.”

Several of her female friends also registered for the hajj this year when they heard the news, wanting to seize the opportunity. While most of their applications weren’t approved by the hajj ministry, the chance to decide on their own whether to apply or not was a welcome change, she said.