The dredge was raised by Canadian army engineers in the early 1990s and restored by Parks Canada.
Dawson City museum director Laura Mann said the closure will affect tourism in the region.
"Tourism brings in an awful lot of money and to see one of the most popular sites being closed I think is bordering on criminal" Mann said.
She was surprised the territorial government didn't respond.
"I would have liked to have seen the Yukon government step in a little sooner and at least express their concern" Mann said.
Yukon tourism minister Mike Nixon says it may not be the end for Dredge 4.
"I think it's departments talking to departments, the federal government talking to the territorial government, it's Parks Canada talking to the community and there's options out there" Nixon said.
He would not give specifics. But he said he'll review visitor surveys to see which options are viable.
The original S.S. Klondike sternwheeler was built in 1929 and the largest riverboat in Yukon. It was replaced with an exact copy after it was destroyed in a fire in 1936.
The second S.S. Klondike operated into the 1950s before being moved onto the riverbank in Whitehorse. It's full of exhibits showing what travel was like in the riverboat days.
It will not be closed, but will offer self-guided tours.