Italy's announcement comes after Chiellini had been reported as a doubt for the two matches, as well as Juventus' Champions League quarter-final first leg against Real Madrid.
Chiellini was taken off during the Serie A match between Juventus and SPAL on Saturday due to a muscular problem.
Juventus will also be anxious over getting the 33-year-old fit for their Champions League quarter-final against Real Madrid with the first leg April 3.
Defender Giorgio Chiellini has been forced to withdraw from Italy's squad to face Argentina and England. The key is to have him fully fit for the visit of Cristiano, Bale, Asensio and the rest on 3 April.
Italy, who have not qualified for the World Cup finals in Russian Federation this summer, will face Argentina at Manchester City's Etihad Stadium on Friday before heading to Wembley to play England a week today.