Director General BSF, Malda Sector, Raj Singh Rathore, said a BSF personnel belonging to the 20 battalion posted at 17 Mile near Farakka, opened fire killing one jawan on the spot.
Four others, who sustained injuries, were rushed to a private nursing home in Malda town, he said.
Officials said the suspected fratricidal incident occurred at the Farrakka battalion camp of the BSF when constable Basant Singh allegedly fired on his fellow personnel who were asleep.
"All have borne bullet injuries fired from the INSAS rifle of Singh. About 4-5 rounds are suspected to have been fired," officials said.
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Singh (35) is on the run and a manhunt has been launched to nab him, they said.
Investigations are on into the incident, Rathore who visited the injured at the nursing home, said.