The accident, which took place days ahead of the annual haj pilgrimage, killed at least 107 people.
The two injured Thais were identified as Maeyoh Taemo, 47, a woman from Pattani, and Sama-ae Shazu, 48, a man from Yala, Vira said, citing a report by Religious Affairs Department director-general Kritsayapong Siri.
The duo received treatment at the Faisal Hospital and were handed over to a medical team at the Royal Thai Embassy.
Haj Affairs of Thailand set up a team to gather information on the incident and help affected Thai pilgrimages.
The Religious Affairs Department has set aside two mobile phone numbers – 094-9520668 and 094-9158257 – for relatives to inquire about Thai pilgrims in Mecca.