Murray missed Sunday's win over the Los Angeles Rams after testing out his hamstring in pregame warmups. Colt McCoy earned the start, but he, too, left the game with a leg injury. Trace McSorley came on to close out the 27-17 win for the Cardinals.
The updates come the same day the team reportedly released backup running back Eno Benjamin and amid a report that starting tight end Zach Ertz (leg) is out for the rest of the season.
Kingsbury said the team wants Murray to be able to go full bore on the field before bringing him back.