The victim, Ramesh Tukaram More, 45, and three other constables were patrolling in a speed boat in the wee hours of Monday at approximately 1.5 nautical miles from the Chitra.
"More fell off the boat after he lost control. The other three constables also could not rescue him as none of them, including the victim, knew swimming," said a police official.
More's body was recovered by life guards later and sent to the state run J J Hospital, officials said.
Two Panamanian cargo ships -- MSC Chitra and MV Khalijia 111 -- collided on Saturday off the Mumbai coast, causing an oil spill from one of the vessels.
Several constables attached with the marine police unit of the city police have been patrolling on speed boats in and around the collision spot since Saturday, officials said.
Oil continued to spill for the third consecutive day on Monday. Anti-pollution operations are being carried out by the Navy and Coast Guard to check the extent of the oil spill and neutralise the oil.
Thirty three crew members, including two Pakistanis, were rescued following the incident.
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