The England international has been plagued by injuries during his Gunners career and has seen his latest comeback derailed after needing to be substituted in the second-half of this week's Carabao Cup semi-final first leg.
Arsenal boss Arsene Wenger has confirmed the 26-year-old has suffered the setback, which is likely to see him miss Sunday's Premier League trip to Bournemouth.
"I don't know if he'll be available on Sunday but it's definitely an ankle sprain," Wenger said.
"At the moment we have five big injuries and we're hoping to get some back. The earliest to come back is [Aaron] Ramsey and that is quite welcome because it's an area we're a bit short.
"If we didn't lose Jack tonight then we would have had Ramsey back and then maybe [Mesut] Ozil on Sunday, but we could look a bit short."