Tensions have been running high since thousands of Rohingya began pouring over the border fleeing a crackdown by the Myanmar army in October, and it is the second time Myanmar forces have fired on Bangladeshi fishermen.
Local police chief Iqbal Hossain said the guards fired on the boat after it allegedly strayed into Myanmar territory today morning.
"Three of the fishermen were injured with bullet wounds. They (fishermen) said they were not aware of crossing Bangladeshi territorial waters," he told AFP.
"The fishermen said they were not given any prior warning before the BGP (Myanmar's border guard police) started shooting," another police official said on condition of anonymity.
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Nearly 70,000 Rohingya Muslims have entered Bangladesh in recent months with stories of killings and mass rape by Myanmar soldiers that have raised global alarm and sparked protests around Southeast Asia.
The army says it is hunting militants behind deadly raids on police posts.
Yesterday Dhaka asked diplomats and UN agencies to back a controversial plan to relocate Rohingya refugees to a remote island.