Lucy Hill, 21, was critically injured when a car and her moped collided on Saturday local time - six days after she arrived in the country.
Fellow Brit Lauren Hall, who had been travelling with Miss Hill, said her friend was in a "critical condition" at Rajavej Hospital in Chiang Mai.
The Leeds Beckett University graduate had undergone brain, pelvic and leg surgery that had left her in need of blood. But Miss Hall said there was a shortage of A negative blood in Thailand.
"There is no blood left for her in the hospital at the moment."
So far Miss Hall's post has been shared thousands of times.
Miss Hall said the response so far has been "fantastic" with lots of expats coming in to offer blood. However, she said it was too early to say if this was enough.
Anyone donating needed to stipulate the blood was to go to Lucy Anne Hill at Rajavej Hospital.
So far $4212 has been raised to help pay Lucy's medical bills.

