"The person was rescued by the local people of the island," the official told Xinhua.
He said Sarwar, 27, informed the rescuers that he was trapped on the island since the day the ferry capsized.
Rescue teams are still struggling to locate the sunken ferry, the official added.
He said the death toll in Monday's ferry capsize in Munshiganj district, 27 km away from capital Dhaka, has risen to 38 after five more bodies were retrieved.
According to the official, some 126 people are still missing.
Many victims are believed to be trapped inside the ferry which sank with some 250 passengers on board.