A bench of Chief Justice Indira Banerjee and Justice M Sundar gave the order while admitting a PIL by 'Fisherman Care', an association of fishermen.
According to the petitioner, on November 13, when five fishermen from the state were fishing at about four nautical miles from Olaikuda near Rameshwaram, a coast guard patrol ship opened fire at them at around 3.15 pm.
One person sustained injuries in the attack, the petition said.
The coast guard personnel also allegedly seized the vessel of the fishermen, the petitioner claimed.
"The Indian Coast Guard which was formed to protect Indian fishermen and assist them in distress has opened fire at the innocent fishermen while they were fishing in Indian waters and indulged in inhuman acts," the petitioner alleged.
The petitioner wanted the court to constitute a special investigation team or to direct an independent agency to probe the issue.
Two fishermen were injured after being hit by a stray bullet allegedly fired during a training exercise by the Coast Guard personnel in the sea off Rameswaram. The Coast Guard, however, denied the incident.