In an Instagram post, the group, which also operates restaurants in Brighton and Hastings, said it had become increasingly difficult to keep the two sites - each of which held between 90 and 100 covers - open amid spiralling costs.
"We have made the incredibly hard decision to permanently close our Southampton and Eastbourne restaurants," the group said.
"It has become increasingly difficult to keep these large units running after such insane price increases such as energy. As an independent business started by two mates, we only ever want to be transparent with you."
Inspired by London’s chicken shop culture, The Bok Shop was founded by Jamie O’Mara and Howard Kaye and opened its first site on Brighton's East Street in 2017.
It went on to launch its second bricks and mortar site in Eastbourne in 2018, with locations in Southampton and Hastings subsequently following last year.
"Over the course of the last few years we have really honed in on what The Bok Shop is, what it means to us and most importantly what it means to our customers," the statement continued.
"We started this journey wanting to combine opening some bad-ass chicken shops with our love for sneakers, gaming and music. What we have built is just that but more importantly a team of incredible people that have showed nothing but resilience and support. This is truly the most humbling part of our journey so far.
"Although it feels like a couple of steps back, it’s all in the name of progress and we’re grateful to have two other awesome shops in Brighton and Hastings that will continue to serve up all of the fried goodness you could ever want."
The impact of inflation and spiralling operating costs has hit the hospitality sector hard in recent months. This week it was also reported that vegan burger restaurant group Frost Burgers had fallen into administration with the closure of its sites in Manchester and Liverpool. The company cited the rising costs associated with running a business as the reason for its collapse.
Earlier in the summer, meanwhile, chef Mark Hix announced the closure of The Fox Inn, the Dorset pub he took on just a year and a half ago, citing rising costs and staffing challenges as the reason.
BigHospitality has contacted The Bok Shop for further comment.