Walcott, 22, returned to London for further "investigation" of the injury, manager Arsene Wenger said, as the Gunners prepare for their opening Premier League game against Newcastle United next month.
"Theo went home early and was due to have an MRI," Wenger said on the club's official website.
"It is an ankle injury that comes and goes. We need some more investigation because sometimes he's completely free of it and sometimes it affects him. But we had to send him back because he couldn't practice anymore."
Wenger also revealed that youngster Conor Henderson - who was stretchered off in Saturday's 2-1 win over Cologne - faces up to six months out after suffering a serious knee injury.
"Conor has a knee injury and it looks as if it is a cruciate. That means unfortunately that he will be out for six months at the very least," Wenger said.