The Coast Guard, however, denied the incident.
The fishermen, identified as Arockiasamy and Johnson from Pamban, were hospitalised, police said, adding, their condition is stable.
The bullet allegedly fired by the Coast Guard is suspected to have been shot off target and hit the duo, who were fishing at nearby Devil's island yesterday.
The stray bullet without gun powder, pierced the upper arm of Arockiasamy and then hit Johnson in his upper limb, police said. However, it was removed from the limb by Johnson himself.
Also Read
According to police, Johnson alleged that the coast guard personnel detained them for several hours for no reason and threatened them with dire consequences if they revealed the alleged firing incident to anyone.
Denying any such incident involving its personnel, the ICG said, "No fisherman has been fired upon by any CG ship in Palk Bay".
It may have be an attempt by the fishermen to "divert" attention as they were checked and warned by the Indian Coast Guard Ship against "unauthorised" paired trawling, the ICG said in a statement.
Alleging that the two men were shot in the Indian waters by the ICG personnel, fishermen's association here sought police action against those who fired at them.
The Coast Guard while denying any firing by its personnel said that the fishing crew in question was involved in "unauthorised" paired trawling.
A Coast Guard vessel on patrol off the International Maritime Boundary Line (IMBL) in Palk Bay "was routinely" investigating fishing boat 'Jehovah Jireh', its statement said.
Paired trawling is not authorised in the state of Tamil Nadu.
"On approaching of the Coast Guard Ship, the fishing boat Jehovah Jireh ran away from the scene by leaving the nets in the water and did not stop despite repeated caution by Coast Guard ship," it said.
During the chase, the fishing boat "also rammed" the ICG ship and was stopped and boarded after 50 minutes, it said, adding the boat crew was interrogated for "running away."
The fishing boat was also cautioned for not stopping for security checks, the statement said.
"It may be an attempt by the fishermen to divert the attention as they were checked and warned by the Indian Coast Guard ship for paired trawling and non-stopping when directed to do so," the statement added.
Disclaimer: No Business Standard Journalist was involved in creation of this content