Carter was not available for comment Thursday, but a spokeswoman for the Carter Center confirmed that the Carters are planning to attend and participate in the build.
Carter, 94, broke his hip this spring when he fell at his Plains home while he was on his way to go turkey hunting.
The first week after his surgery, he was forced to bow out of the Sunday school class he normally teaches. But he's made a quick recovery and returned to teaching at Maranatha Baptist Church less than a month later.
He also made the trip to Leesburg, Virginia, for the Carter Center's annual five-day retreat.
The build in Tennessee comes at a time when the Southern city is struggling to find ways to come up with affordable housing to keep up with Nashville's recent growth. Though the boon has brought more jobs and opportunities, it has also meant an increase in housing prices, which has left low-income residents struggling.
In March, Mayor David Briley unveiled his Under One Roof 2029 initiative.
The city plans to invest $750 million over the next decade to build 10,000 affordable housing units across the city.