Brookes suffered the injury in Saints' defeat to Worcester Warriors last weekend and, after being assessed, is expected to be on the sidelines until early January.
Jamal Ford-Robinson is set to get a chance in his absence against Sale Sharks on Saturday, while George North (knee) and David Ribbans (ankle) are both still out.
Northampton sit eighth in the Aviva Premiership after eight games, winning four and losing four so far, and take on a Sale outfit who are below them in the table.
The Sharks are 10th with just two victories to their name this season.
Meanwhile, Saints have released lock Josh Peters after the 22-year-old failed to force his way into the senior set-up at Franklin's Gardens.