Chiellini suffered the injury during Saturday's goalless draw with SPAL, and Juventus revealed on Monday that the centre-back would be unavailable to take part in Italy's international friendlies with Argentina and England.
The 33-year-old's injury has been described as "not serious", but the Italian champions have not put a timeframe on the defender's return to the field.
"The tests revealed that Chiellini's injury, while not serious, will require daily monitoring. The defender has started undergoing physiotherapy and his condition will be re-evaluated next week," read a statement from Juventus.
Juventus will take on AC Milan in their next Serie A match on March 31, before hosting Real Madrid in the first leg of their Champions League quarter-final on April 3.