The 29-year-old Spain global left the pitch midway through the first-half of the 3-0 friendly win over the Gunners at Beijing's Bird's Nest Stadium after a heavy collision with goalkeeper David Ospina.
Conte says the 29-year-old will stay in hospital for observation, but hopes he will link up with the rest of the squad on Sunday in Singapore for the International Champions Cup clash with Bayern Munich next week.
Conte had initially hoped the Spain worldwide would be fit enough to make the next leg of the pre-season tour but the 29-year-old was sent home due to severe concussion.
"The situation was more serious than I thought because I hoped it would only be concussion and instead he had multiple fractures", Conte said.
The Blues boss reserved praise for his two-goal striker, who moved to Stamford Bridge from Marseille last summer.
However, Conte also made a point to add that his side has no "ill-feeling" toward Ospina as a result of the recent incident. "Pre-season is very important", he said.
"It is good to have this type of start but we have to continue to work a lot to improve on the physical and tactical aspect".
After threatening to break the deadlock early in the game, Chelsea finally grabbed the lead inside a packed Bird's Nest Stadium when winger Willian netted his fourth goal of the young pre-season for the Blues.