It is the 17th league game to be postponed due to COVID-19 cases and injuries. The Premier League only grants a postponement if a club has fewer than 14 players -- 13 outfield players and one goalkeeper -- available, with the board examining requests on a case-by-case basis.
"The Board accepted Norwich's application as the club do not have the required number of players available for the match [13 outfield players and one goalkeeper], due to COVID-19 cases and injuries," the league said in a statement.
Norwich had their game at West Ham United postponed due to COVID-19 cases, injuries and illness reported among players and staff, while Leicester had matches against Tottenham Hotspur and Everton postponed due to coronavirus cases among their players.
"Those individuals who have returned a positive COVID-19 test result are completing a period of self-isolation, as per Premier League protocols and government guidelines," Norwich said.
"The club regrets any inconvenience caused to Leicester City and both sets of supporters."
Earlier Thursday, Leicester had said Jamie Vardy would be out a month because of a hamstring problem suffered in Tuesday's 1-0 win over Liverpool, intensifying the team's injury crisis. It leaves Leicester with a striker shortage, with Patson Daka also injured and Kelechi Iheanacho set to depart for the Africa Cup of Nations next week.
Leicester boss Brendan Rodgers said the packed festive schedule and the extra demands placed on players due to COVID-19 had played a significant part in Vardy's injury.
"I think the fatigue element in that combination of games has probably led to it,'' he said. "The players are not robots. People think because they are paid a lot of money they should turn out and play every single day of the week and that's not the case."
Information from Reuters and The Associated Press was used in this report