The incident happened on Friday night, the Al-Riyadh newspaper said, as the pilgrims gathered in large numbers to mark the Night of Destiny, one of the high points of Ramazan.
All the injured were treated at the scene and none required admission to hospital, the newspaper cited a health official as saying.
Hajj pilgrims to get e-bracelets for safety
Every year, hundreds of thousands of pilgrims flock to Makkah to carry out umrah pilgrimage during Ramazan -- especially during its last 10 days.
They include the Night of Destiny, when the angel Gabriel is believed to have given the Prophet Mohammed (PBUH) the verses of the Quran.
The incident comes as Saudi authorities continue to unveil new safety measures for this year's Hajj in September.
A crush at last year's Hajj killed more than 2,000 pilgrims in the worst disaster to ever strike the annual ritual.
Saudi Arabia 'alarmed and outraged' by rights groups' criticism
According to figures from foreign officials, at least 2,297 pilgrims died. Saudi Arabia issued a death toll of 769.
Newspapers reported on Friday that, among new security measures, Hajj pilgrims this year will have to wear an electronic safety bracelet to store their personal information, including address and medical records.
The Hajj and umra pilgrimages bring millions of Muslims to the holy places in Saudi Arabia every year.
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