Horticultural tasks such as pruning and selective harvesting are labor intensive and horticultural staff are hard to find. Automating these tasks is challenging due to the semi-structured greenhouse workspaces, changing environmental conditions such as lighting, dense plant growth with many occlusions, and the need for gentle manipulation of non-rigid plant organs. In this work, we present the three-armed system HortiBot, with two arms for manipulation and a third arm as an articulated head for active perception using stereo cameras. Its perception system detects not only peppers, but also peduncles and stems in real time, and performs online data association to build a world model of pepper plants. Collision-aware online trajectory generation allows all three arms to safely track their respective targets for observation, grasping, and cutting. We integrated perception and manipulation to perform selective harvesting of peppers and evaluated the system in lab experiments. Using active perception coupled with end-effector force torque sensing for compliant manipulation, HortiBot achieves high success rates.