Mexican Official Ricardo de la Cruz Musalem said the injured had been transferred to hospitals, including some by air.
Since April, dozens of female soldiers have become part of the security services that monitor pilgrims in Mecca and Medina.
Two of Islam's holiest sites, Mecca and Medina, are now open to Muslims living in Saudi Arabia, after a 7-month Covid-19 pause.
Hajj pilgrimage is usually one of the world's largest religious gatherings but this year only up to 10,000 people already residing in the kingdom will participate in the ritual as the Saudi hosts try to prevent the spread of virus pandemic.
The accident occurred at an unmanned railway crossing close to the city of Sheikhupura in Pakistan's largest province, Punjab.
Hundreds of thousands of Hindus are celebrating the annual Thaipusam festival which sees devotees carrying offerings to places of worship and piercing their skin with hooks and skewers to show devotion to Murugan.
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