Perez and his wife, Melanie, were released on personal bond, police said. A message was left with his attorney Friday; the player and the lawyer haven't responded to previous requests for comment.
A message seeking comment was left Friday with the team. Team officials earlier said they were watching the situation.
Dan Chaplin, a Cleveland defense attorney not connected with the case, compared the charge to a traffic ticket and said a conviction likely would be punished with a fine.
Drug agents with a search warrant went to the couple's rental home on Tuesday, apparently tipped off by postal workers suspicious of a package mailed there.
Perez has six saves this season but is on the disabled list with an injured right shoulder. The right-hander started throwing again this week.
Perez, an often-polarizing figure, and Cleveland fans have gotten on each other's nerves over the past couple of years. He recently deactivated his Twitter account after criticism from fans following a couple of bad outings.
In previous seasons, Perez has lashed out at fans for not coming to games, and at owners for not spending money on free agents.