Langmead underwent surgery on Thursday after a knee injury forced him off after just 12 minutes of the Cobblers' 1-0 home win over Oxford last weekend.
The centre-half, who had been an ever-present in Aidy Boothroyd's team this season prior to that, is expected to regain fitness before the end of the campaign.
Nathan Cameron has been drafted in as cover for Langmead and the 21-year-old, on loan from Coventry, will compete with Lee Collins for a starting role against the Gulls.
John Johnson was also withdrawn against Oxford because of a hamstring strain but the right-back will be fit for Friday night's fixture.
Midfielder Chris Hackett has been playing despite a slight calf strain and Cobblers boss Boothroyd may opt to rest him at some point over the Easter schedule with two matches in the space of four days.