Forest canopies are vital ecosystems, but remain understudied due to difficult access. Forests could be monitored with a network of biodegradable sensors that break down into environmentally friendly substances at the end of their life. As a first step in this direction, this paper details the development of a biodegradable origami gripper to attach conventional sensors to branches, deployable with an aerial robot. Through exposure to sufficient moisture the gripper loses contractile force, dropping the sensor to the ground for easier collection. The origami design of the gripper as well as biodegradable materials selection is detailed, allowing for further extensions utilizing biodegradable origami. Both the gripper and the gelatin hydrogel used as an actuating elastic element for generating the grasping force are experimentally characterized, with the gripper demonstrating a maximum holding force of 1 N. Additionally, the degradation of the gripper until failure in the presence of moisture is also investigated, where the gripper can absorb up to 10 ml of water before falling off a branch. Finally, deployment of the gripper on a tree branch with an aerial robot is demonstrated. Overall, the biodegradable origami gripper represents a first step towards a more scalable and environmentally sustainable approach for ecosystem monitoring.