Branches in Northampton, Corby, Kettering and Rushden will stay open.
Daventry customers' nearest HSBC branch after September will be nine miles away in Rugby.
HSBC bosses announced closures of 69 branches as part of a "transformation programme" across the UK, saying it would increase the average distance customers needed to travel by three-tenths of a mile.
In a statement issued on Tuesday (March 15), Jackie Uhi, head of HSBC UK’s Branch Network, said: “The way people bank is changing, something the Covid pandemic has accelerated.
"Our branches continue to support people with their more complex banking needs, but the way we can do this has also evolved, with the addition of banking hubs, community pop ups and continued use of the Post Office network.
"Rather than a one-size fits all branch approach, it’s an approach built around the way different customers are choosing to bank in different areas.
“We know the majority of our customers have a preference to do much of their day-to-day banking online or via mobile, so we’re removing locations where we have another branch nearby, and where there is a significant reduction in customers using face-to-face branch servicing.
"This will enable us to invest in locations where our customers are continuing to utilise the branch network, including updating technology and refurbishing.”
Fewer than half of HSBC customers now actively use its branch network with the average footfall declining more than 50 percent since 2017, according to the bank.
HSBC is the latest among the major High Street banks to shut branches.
Barclays closed in Weston Favell, Daventry and Towcester earlier this month.