Coast Guard officer Jeff Olsson said the tug was working with a second tug manoeuvring a barge on the fast-flowing river just up from the CNR Rail Bridge when it flipped and capsized.
The tug was reportedly towing a barge from Amix Recycling's Surrey location.
Olsson said the captain swam for shore and was helped by someone on a nearby boat.
The other person was on the barge, which broke loose when the tug sank and floated downstream.
Olsson said that person was rescued by the second tug.
Both the captain and the person on the barge have been taken to Royal Columbia Hospital.
The barge has since been secured.
The Coast Guard is at the scene and is attempting to locate the sunken tug.
The lower Fraser River flood waters are nearing their peak, and Olsson said the water is flowing so quickly that Coast Guard crews had little time to attempt a rescue.
The B.C. River Forecast Centre has issued a high stream flow advisory for the lower Fraser, which is being fed by a high flow from the Thompson River. The lower Fraser's flow is expected to peak this weekend.