Piezoelectric III-N semiconductor nanostructures are of increasing interest to be used for sensor technologies and energy harvesting. Within this group of materials, AlN is known for the largest bulk piezoelectric constant, but piezoelectric properties of AlN nanostructures are not well studied. In the current work, AlN nanostructures are fabricated by reactive magnetron sputter deposition at normal and glancing angle orientations on Si substrates covered by a conductive TiN film. Ag nanoparticles are used to facilitate nucleation of the nanostructures, which are found to have a bud-like shape consisting of individual pillars/lamellae. These pillars exhibit a wurtzite-like hexagonal lattice and preferential growth direction along the c-axis. Piezoresponse force microscopy is used to characterize the properties of the nanostructures. Giant values of the piezoresponse coefficient are measured, reaching up to 6 times higher values compared to AlN bulk and thin films. The obtained results create a basis for optimization of the fabrication parameters enabling tuning of the AlN piezoelectric properties and further development of the technology toward the formation of large-area nanoscale matrixes for energy generation.