Aims. We investigate the spatial distribution of dust emission around Tycho's SNR to understand its origin. We distinguish the dust associated with the SNR from that of the surrounding ISM. Methods. We performed mid-to far-infrared imaging observations of the remnant at wavelengths of 9, 15, 18, 24, 65, 90, 140, and 160 μm using the Infrared Camera and the Far-Infrared Surveyor onboard AKARI. We compared the AKARI images with the Suzaku X-ray image and the 12 CO image of Tycho's SNR. Results. All the AKARI images except the 9, 140, and 160 μm band images show a shell-like emission structure with brightness peaks at the northeast (NE) and northwest (NW) boundaries, sharply outlining part of the X-ray shell. The 140 and 160 μm bands are dominated by cold dust emission from the surrounding ISM near the NE boundary. Conclusions. We conclude that the dust emission at the NE boundary comes from the ambient cloud interacting with the shock front, while the origin of the dust emission at the NW boundary is rather unclear because of the absence of prominent interstellar clouds near the corresponding region. We cannot rule out the possibility that the latter is mostly of an SN ejecta origin.