Yes. When a tsunami reaches shore, its long wavelength allows it to surge far up river channels and estuaries, flooding inland areas. The narrow, shallow river amplifies the wave—making it higher, faster, and more destructive.
Historic examples: 2011 Tohoku tsunami penetrated 40+ km up Japan's Kitakami River; 2004 Indian Ocean tsunami surged up Sumatra's rivers. Flooding damages bridges, roads, buildings, and ecosystems, and endangers communities far from the coast.
Mitigation: seawalls, levees, floodgates, early warning systems, evacuation planning, and restricting development in vulnerable floodplains.