Bernd Leno came on to make his debut and will seek to impress coach Unai Emery as he eyes an extended run in the starting line-up.
An update from Arsenal's medical team on Tuesday confirmed Cech's anticipated period of absence.
"Expected to return to full training in three to four weeks," the statement said of Cech's hamstring injury.
Arsenal added that Laurent Koscielny's recovery from an Achilles injury is progressing well.
The France centre-back, who missed the World Cup, could return to full training next month.
The news will come as a blow to Emery, who had previously speculated that the former Chelsea man could miss as little as a fortnight .
"I don’t know [when Cech will return now," he told the media after the Watford game on Saturday. "We will look tomorrow.
"I hope not more than maybe two or three weeks he can stay with this injury. It’s muscular. I think [it is a hamstring problem]."
Emery's men, who have won seven games in a row, face Europa League clashes with Qarabag and Sporting CP in October, along with Premier League matches against Fulham, Leicester City and Crystal Palace.
It’s wrong guys ... I’d wear a tie pic.twitter.com/0qGSK3TvHg— Petr Cech (@PetrCech) September 27, 2018
Arsenal will also be active in the Carabao Cup over the course of a packed month, as they gear up for a fourth round clash at home to Blackpool.