First baseman Alonso left in the third inning of Tuesday's game with lower-back tightness. In a play at the plate in the seventh inning, Norris sustained a left-shoulder and elbow hyperextension, and moments later reliever Kelley left the game with right-forearm tightness.
"Luckily it doesn't look like any of them look that serious," interim manager Pat Murphy said Wednesday. "You will see those guys back in the lineup before long."
Assistant general manager Josh Stein said that the team came out of Tuesday's game fortunate in regards to the injuries.
Dickerson, who was named Pacific Coast League's Rookie of the Year on Tuesday, will make his second stint with the Padres this season.