Left-back Alex Sandro suffered a medial collateral ligament injury during Juve's defeat to Napoli in the Coppa Italia final.
The Brazil international's knee problem could reportedly keep him sidelined for three weeks.
Khedira damaged his thigh in the warm-up ahead of a drab final at Stadio Olimpico, where Napoli won 4-2 on penalties after a goalless 90 minutes.
Juve did not specify how long the duo will be out of action four days before their first Serie A match since the season was suspended in March due to the coronavirus crisis.
A club statement said: "Diagnostic tests carried out at J-Medical this afternoon [Thursday] showed for Alex Sandro, a first-degree lesion of the medial collateral ligament. Physiotherapy began immediately.
"For Khedira, a partial injury of the tendon on the long adductor muscle of the right thigh. In the coming days he will undergo further investigations to define recovery times.
"Personalised work for Giorgio Chiellini and Gonzalo Higuain also continues. Training is scheduled for Saturday afternoon."
The Turin giant is top of the table with 12 games remaining, just a point ahead of Lazio.