"What a shock! Fortunately everything is ok", Pedro tweeted after he was rushed to hospital.
Asked if the challenge was a fair one, he told reporters: "No, absolutely not".
"He will now return to London for further review", the club added.
"It was a bit of a combination for us, I think it was a good opportunity for me to see players at that level who have no experience".
The Spaniard was chasing a through ball when he was clattered by Ospina during the Colombian's follow through, with Pedro taking a blow to the head and neck.
The Spanish also posted on social media that "everything is OK".
Eden Hazard is injured after breaking an ankle training with Belgium at the end of last season and is not expected to be fit until the end of September.
The rest of the Chelsea squad are now in Singapore where they will play two games - against Bayern Munich on Tuesday and Inter Milan on 29 July.
With Diego Costa apparently on his escape at Stamford Bridge, it was simply the performance he had to reveal Conte that he could test new signing Alvaro Morata for a first string berth this period.