The number who have fled since communal violence broke out two years ago has now topped 100,000.
Chris Lewa, director of the nonprofit Rohingya advocacy group Arakan Project, said an average of 900 people per day have been piling into cargo ships moored off Rakhine state since the 15th of October.
Lewa said Friday that some Rohingya families have been told the huge cargo ships already have started arriving in neighboring Thailand, where Rohingya face deportation or fall victim to human trafficking.
Lewa also said a number of Rohingya were also moving overland to Bangladesh and on to India and Nepal.
Myanmar is a Buddhist nation of 50 million including an estimated 1.3 million Rohingya, who are known to have arrived from neighboring Bangladesh generations ago.
The Rohingya have been denied Myanmar citizenship and have been attacked by Buddhist mobs, which has left hundreds dead and 140,000 trapped in camps.
The majority live in the northern tip of Rakhine state, where an aggressive campaign by authorities in recent months to register family members and officially categorize them as "Bengalis", implying they are illegal migrants from neighboring Bangladesh.
Rohingya villagers who spoke to the Associated Press news agency said that some of them were confined to their villages for weeks at a time for refusing to take part in the "verification" process; others beaten or arrested.