One of the men was injured by shrapnel from shots fired by the Coast Guard to disable the boat's engines, Coast Guard officials said.
The injured man was one of several people aboard a type of speed boat known as a go fast in international waters some 60 miles off the coast of Colombia when the craft was spotted by counter-narcotics boats patrolling in the region.
A U.S. Navy aircraft with a U. S. Coast Guard gunner aboard launched from a Navy ship, pursued the suspected smugglers, signaled the boat to stop and fired warning shots in front of the go fast.
However, the vessel's crew, which had been observed throwing bales out of the boat, refused to stop.
The pursuit ended after approximately 20 minutes when the Coast Guard sharpshooter was authorized to direct disabling fire into the fleeing vessel's engines to force the craft to halt, officers said.
The tactic worked, and the vessel halted, but it was then discovered that one of the suspected smugglers was injured.
A Coast Guard boarding team, including an emergency medical technician, launched from the U.S. Navy ship.
They arrived and treated the man.
He was taken on the boarding team's boat to the Navy ship for further treatment by the vessel's medical staff.
Once aboard the Navy ship officers determined his injuries warranted further transfer to a hospital ashore.
A U.S. Coast Guard helicopter operating from a Coast Guard cutter on patrol in the area moved the man to Buenaventura airport in coordination with Colombian authorities.
Smugglers often sink their own boats or jump into the sea to avoid discovery or capture.
Coast Guard officials said they were conducting a review of what happened to make sure the drug bust was executed correctly.
Bales of cocaine from the boat have since been collected by representatives of both the U.S. and Colombia as evidence for future prosecution.
The go-fast boat has not been located and is believed to have sunk, officials said.
As of Wednesday morning Colombuan authorities reported to the U. S. Coast Guard that the injured man was in stable condition.
U. S. Coast Guard records indicate there have been 63 cases where disabling fire from a helicopter was used to damage a fleeing boat' engines since the tactic was first tested in the late 1990's.
Shrapnel injuries to smuggling boat crews in connection with the tactic are rare, officers said.
Sunday's incident was the fifth such case. Information on the extent of the injuries involved in the previous four was not immediately available.