The arrests come amid mounting fears for the country's dwindling tiger population after research showed their number had fallen to fewer than 1,500, from 3,642 in 2002 when the last survey was conducted.
"We have recovered three tiger skins and 75 kilogrammes (165 pounds) of bones. We arrested 16 people," police official Amitabh Yash told AFP.
Twelve people were being held for trading tiger parts, he said, and the rest for hunting the big cats in northern Uttar Pradesh state.
He said the pelts and bones were probably destined for China, where they are believed to have medicinal properties.
Tiger hunting is illegal worldwide and the trade in tiger body parts has been banned since 1993.
India has faced heavy criticism from wildlife experts for failing to stop rampant poaching.