The sculpture appeared just north of the Madison Street bridge, created by an artist identified only as "The Phoenix," the Eau Claire Leader-Telegram reported.
The Department of Natural Resources ordered the sculpture removed, saying it poses a navigation hazard.
In e-mail to the newspaper, a person identifying himself as the artist said he would remove the sculpture within the next 10 days because "as much as I would like to leave it there, I don't want the DNR finding out it was me and fining me for it."
The Phoenix may have a paying customer for the work. The home improvement chain Menards, which has its corporate headquarters in Eau Claire, said it could give the sculpture a home.
"We have ponds and fountains on many of our properties, and seeing this piece of artwork in the Chippewa River spurred some conversation," Menards spokesman Jeff Abbott said in an e-mail message to the Leader-Telegram.