Mayo spokesman Nick Hanson said he did not know where Jackson was going after he left the Minnesota hospital.
Jackson returned to the hospital in October amid reports that he faced a new federal investigation into potential misuse of his campaign finances.
He remains under a U.S. House committee’s investigation into his dealings with imprisoned former Illinois Gov. Rod Blagojevich.
Nonetheless, Jackson was elected Nov. 6 to a ninth full term representing his Chicago area district, despite his not campaigning and barely appearing in public since taking medical leave in June.
Jackson was treated at the Mayo Clinic last summer for bipolar disorder and gastrointestinal issues. After he returned to the hospital, his father, the Rev. Jesse Jackson, said his son had not yet "regained his balance."
On Tuesday, Illinois Gov. Pat Quinn became the latest elected official to urge Jackson to talk to the public about his condition. Chicago Mayor Rahm Emanuel called on Jackson on Monday to "have a conversation with his constituents about his intentions" now that the election is over.