Recently, the octonion Fourier transform (OFT) has been proposed and utilized in image processing. This transformation is intimately related to the three-dimensional Clifford Fourier transform. Similar to the Clifford Fourier transform, the uncertainty principle is recognized as an important result in the OFT. The present study explores Heisenberg-type inequality associated with the OFT. This uncertainty principle describes how an octonion-valued signal and its OFT relates. Variations on the uncertainty inequality are then established. Finally, we establish a new form of Heisenberg uncertainty principle for octonion linear canonical transform (OLCT). This result refines Heisenberg inequality for the OLCT in literature.