Smith, who took over for Ryan in 2007, was released after a season where Minnesota was last in the American League Central, 32 games back of the division-leading Detroit Tigers.
"No one in the Twins' organization wants to win any more than Bill," Twins owner Jim Pohlad said in a statement.
"He is unquestionably loyal, committed and talented. The Twins goal is to get better in 2012 and beyond. Bill was equally motivated to achieve that goal but we differed in the scope and approach that was required."
Pohlad also said the team intends to have additional talks with Smith, who has been with the club since 1986, about an ongoing role with the Twins.
Ryan, 58, has spent over 28 years with the Twins, including a stint as general manager from 1994-2007. His interim role is effective immediately.
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Frank Pingue)