The development of reliable fruit detection and localization systems is essential for future sustainable agronomic management of high-value crops. Up to date, most proposed systems on fruit detection and characterization are based on RGB cameras and thus affected by intrinsic constraints, such as variable lighting conditions and camera calibration. This work presents a new technique that uses a mobile terrestrial laser scanner to detect and localize fruits regardless of the prevailing lighting conditions and without the need of a previous calibration. An experimental test focused on two Fuji apple trees (containing 139 and 145 apples each) was carried out. A 3D point cloud of this scene was generated using a Velodyne VLP-16 LiDAR sensor synchronized with a RTK-GNSS receiver. A reflectivity analysis of tree elements was performed, obtaining mean reflectivity values of 28.9%, 29.1%, and 44.3% for leaves, trunks, and fruits, respectively. These results suggest that the reflectivity parameter can be useful to localize fruits in the tree. From this knowledge, a three-step fruit detection algorithm has been developed: 1) reflectivity thresholding to remove most of the leaves and trunks from the original point cloud; 2) statistical outlier removal to reduce noise; 3) connected components clustering using a density-based algorithm. By applying this algorithm to our dataset, a localization success of 85%, a detachment success of 78.8%, and a false detection rate of 15.2% were obtained. These detection rates are similar to those obtained by current RGB-based system, but with the additional advantage of providing direct 3D fruit location information (global coordinates) which is not affected by sunlight variations. It can be concluded that LiDAR technology and, particularly, its reflectivity information, might have potential use in fruit detection. Future work should include the application of this fruit detection technique on a wider range of crop types