Marine Animal Response Society co-ordinator Tonya Wimmer said the whale was first spotted near Eastern Passage on Monday evening. By Tuesday, it was in the Bedford Basin.
It was last seen at 11 a.m. on Friday.
Jamie Osborne, a fisherman, filmed the beluga from onboard his boat on Monday evening. He stopped his boat 200 to 300 metres from the government wharf in Eastern Passage to take in the unusual sight.
"Never see something like that again here, I don't imagine. I was surprised to see it. I don't know if it was the cold water or why it's here," he said Friday.
Osborne said he thinks the harbour is colder than it normally is at this time of year.
"When I first seen it, it was right in the sun. I didn't know it was white. So I went over there in the boat just to have a look," he says. "He swam right up to me. For a half hour or so, I sat there."
Wimmer and the department are warning people who may be out on the harbour to stay away from the whale.
"It's a potentially dangerous situation for the animal and the public," she said, adding that anyone who sees it should call the Marine Animal Response Society at 1-866-567-6277.
Wimmer says the whale most likely came from the endangered St. Lawrence population of beluga whales.
"Every now and then they have juveniles who go for a wander," she said. "Occasionally they end up in harbours."