The Coyotes said Ballard will be sidelined for up to five weeks after fracturing a bone in his hand during Monday night's 5-1 loss at Columbus.
Ballard, who played all 82 games as a rookie last season, blocked a shot with his right hand in the first period and missed the rest of the game.
He returned to Phoenix to be examined by team doctors, and the fracture was detected. It is not yet known if Ballard will need surgery.
Yandle, one of the Coyotes' final pre-season cuts, had two assists and four penalty minutes in two games with the Rampage this season.
The 20-year-old Yandle, a Boston native, is in his first professional season after leading CHL defencemen in scoring. He was chosen as the league's top defenceman last season.