Kidd, who missed Tuesday's game and was also out for Wednesday's contest, had not sat out a game because of injury or illness since Dec. 4, 2004.
He was selected an All-Star for the eighth time after averaging 14.3 points, 8.7 assists and 8 rebounds a game this season.
"It was an honor to be selected by the coaches to participate in this year's All-Star Game," Kidd said. "However, my injury needs rest in order to heal properly, so I will unfortunately not be able to play."
Kidd will be replaced in the Eastern Conference All-Star lineup by Atlanta Hawks guard Joe Johnson. It is the first All-Star selection for Johnson, who leads the Hawks averaging 25.1 points-per-game.
The NBA All-Star Game is Sunday in Las Vegas.