At least 200 Rohingya have drowned since late August making the treacherous sea crossing from Myanmar to Bangladesh.
Overall, some 600,000 members of the Muslim minority have fled their mainly Buddhist homeland following a wave of violence there which the United Nations has described as ethnic cleansing.
Police said the three babies fell into the water as their boat reached shore in the town of Teknaf on Monday evening.
The other four victims drowned when their boat sank in rough weather on Tuesday morning as it neared the Bangladesh coast.
"There were at least 33 people in the small trawler, which capsized after it was caught in high waves," local police chief Abul Khair told AFP.
He said one person was found dead at the scene while six others were rushed to hospital in critical condition. Three of them later died.
The rest were dragged ashore or managed to swim to safety, Khair added.
Most have crossed by land into Bangladesh, where refugee camps have been overwhelmed by the sick and injured.
But others have made the dangerous voyage by sea, taking rickety fishing boats into the Bay of Bengal and snaking up the coastline of Bangladesh looking for a spot to make landfall.
The refugees have described systematic massacres, rapes and arson in their villages by Myanmar troops and ethnic Rakhine Buddhists.
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