Walsh will then start his new private-sector job as executive director of the NHL labor union, the hockey news website reported.
The NHL Players' Association did not respond to a request for comment.
Deputy Labor Secretary Julie Su, a former California labor secretary, is expected to take over as acting secretary.
As Labor secretary, Walsh had vowed to boost union membership, a key issue for Biden.
The NHL players' union represents 750 athletes, according to the organization.