Graham was outrighted to Triple-A on Monday.
Graham was traded to the Yankees on Saturday for a player to be named later or cash considerations.
Graham was designated for assignment Friday, LaVelle Neal of the Minneapolis Star Tribune reports.
Graham will be recalled by the Twins, LaVelle E. Neal of the Minneapolis Star Tribune reports.
Graham was optioned to Triple-A Rochester.
Graham lost around 30 pounds during the offseason but it hasn't impacted his velocity as he topped out at 96 mph on fastballs in Wednesday's spring outing, the Minneapolis Star Tribune reports. "He's still got his velocity," Molitor said. "We were wondering how the ball was going come out of his hand this spring after his, transformation, if you will. Things have been fairly clean so far."
Graham (shoulder) was activated from the DL on Friday.
Graham (shoulder) threw a full 30-pitch bullpen session Friday and is on track to come off the DL during next weekend's series in Chicago, Mike Berardino of the St. Paul Pioneer Press reports.
Graham was placed on the 15-day DL on Wednesday, Rhett Bollinger of MLB.com reports.