General manager Rick Spielman announced that the Vikings will not resign Peterson to a contract for the 2017 season. Minnesota did not say whether they offered the 31-year-old Peterson any type of deal.
"With us signing Murray, Adrian will move on elsewhere," Spielman said.
Peterson leaves the Vikings as one of the best players in club history. The four-time all-pro had seven 1,000-yard rushing seasons in nine years, but battled injuries the past few seasons.
The unrestricted free agent is the Vikings' career rushing leader with 11,747 yards and 97 touchdowns.
"Adrian is probably going to go down as one of the greatest Vikings," Spielman said.
Peterson's future is now in limbo -- he had visited Seattle, but the Seahawks passed on him.
In 2012, Peterson came within eight yards of Eric Dickerson's single-season rushing record of 2,105 yards set in 1984.