A series of coordinated attacks by Rohingya insurgents on security forces in the north of Myanmar's Rakhine state on Friday and ensuing clashes triggered the exodus, while the government evacuated thousands of Rakhine Buddhists.
The IOM said it was difficult to estimate the number of people stranded in the no man's land at the border between the neighbors, but added there were "hundreds and hundreds" of people stuck there.
The treatment of about 1.1 million Muslim Rohingya in Myanmar has become the biggest challenge for leader Aung San Suu Kyi, who has been accused by Western critics of not speaking out on behalf of a minority who have long complained of persecution.
The Rohingya are denied citizenship in Myanmar and regarded as illegal immigrants, despite claiming roots there that go back centuries.