The man was seen dog paddling before disappearing from view downstream under the bridge. There were no further sightings.
The man who jumped was described as Maori or Pacific Islander aged about mid-30s, 178cm tall and skinny build with straight black, shoulder length hair. He appeared to have a goatee-type beard, thin facial features and was wearing a red baggy T-shirt with long blue/black pants.
Detective Karl Little is hoping the excellent description will resonate with someone in the community.
"We appeal to anyone who may have jumped off the bridge at that time, or anyone who may have a loved one missing, or may have witnessed the incident, to come forward. It is possible the man exited the river and told a friend or family member of his experience.
"Either way we want to resolve the incident," he said.
Anyone with information can phone Detective Little at Hamilton Central Police Station on 858 6315.