The medal was stolen from Visva-Bharati University in West Bengal in March 2004 and Indian police believe it may have been taken to Bangladesh.
On Saturday, police raided a house in Dhaka's Azimpur area and arrested Mohammad Hossain Shiplu who is accused of close links with the main Indian suspect Jibon Singh.
"The raid was conducted following a tip from Indian police," said Abdullah Aref, a senior official of the Criminal Investigation Department.
Singh is believed to be hiding in Bangladesh.
Bengali poet Tagore won the Nobel Prize in literature in 1913.