Pedro was withdrawn from the Beijing encounter with a suspected concussion after a collision with Gunners goalkeeper David Ospina. He was taken to a local hospital for checks and then returned to London as a precaution while the rest of the squad advanced to Singapore.
Speaking to the media in Singapore, Conte explained that Pedro has actually suffered 'multiple fractures' in a cheekbone injury.
That means he won't be able to train for around 10 days and will have to wear a protective mask - as he has done once already in his Chelsea career - when he returns to action early next month with the rest of the squad after the conclusion of the Asia tour.
It comes as a setback for Chelsea with Eden Hazard already ruled out of action after he suffered a broken ankle while training with the Belgium national team in June.
Hazard took to Instagram over the weekend to post a video of him training at Chelsea's Cobham base as continues his rehab, shared with the caption 'The recovery continues'.
Chelsea face further games on tour against Bayern Munich and Inter Milan in the International Champions Cup, before meeting Arsenal again in the Community Shield at Wembley.