An implant for insertion through a punctum and into a canalicular lumen of a patient. The implant includes a matrix of material, a therapeutic agent dispersed in the matrix of material, a sheath disposed over a portion of the matrix of material and configured to inhibit the therapeutic agent from being released from the matrix of material into the canalicular lumen and to allow the therapeutic agent to be released from a surface of the matrix of material to a tear film, and a retention structure configured to retain the implant within the canalicular lumen.