Jesus, 25, is already out for about four weeks and is set to fly back to the UK to be evaluated by Arsenal doctors after leaving Brazil's World Cup camp.
According to sportv, if the forward ends up needing surgery then he will be sidelined for at least the next three months.
The striker appeared to confirm his injury, tweeting: "If there was a timeline and I could see you and tell you something, I would say 'Gabriel, you are a winner'.
"Thank you to everyone who sent messages of support and affection."
It will come as a massive blow to Arsenal's title hopes, with Jesus being an integral part of the Gunners' unexpected title charge.