Debbie Bartley Williams died after the group arrived in Chile, according to Dr. Greg DeLoach, the pastor of the church. The cause of death was not immediately known.
Williams, 59, was accompanying her husband, Dr. George Williams of Obstetrics and Gynecology Associates of Augusta.
She felt ill during the flight and was rushed to the hospital after the plane touched down in Puerto Montt, DeLoach said.
"It is very tragic," he said. "There's no positive spin on this. You're going to do a mission trip in the wake of tragedy and then tragedy happens to strike."
A team of nine, including five doctors, left from First Baptist on Friday to serve in clinics needing help after February's earthquake. They will continue on as planned, though Williams' husband will return early.
A small memorial was held at a Chilean church, but funeral arrangements in Augusta aren't finalized.
The team headed first to meet the daughter of one of First Baptist's pastors, the Rev. Rodger Murchison. She's married to a missionary in Chile.
They will continue on to Los Muermos. During the week, they will work in a girls' home, speak in a church and visit a nature preserve before returning home March 29.
The team's members attend First Baptist, Reid Memorial Presbyterian and St. Paul Episcopal churches. Most have served on international missions before, Murchison said. The Williams family participated in missions as far away as west Africa, Hungary and Brazil.
"Debbie was such a servant. There isn't any bit of First Baptist Church that hasn't been touched by her," said Cynthia Bennett, a friend at the church for more than 20 years. "We're just devastated. We're trying to make sense of this."
DeLoach described Williams as an active, contributing member of the congregation, both in missions and church life.
"Debbie was a very thoughtful, an incredibly giving person. She operated off a very high ethic of 'To whom much is given, much will be required,' " he said. "She served in just about every area possible. She was very creative. Her background was in theater, and any kind of production we put together, she was the energy behind it.
"I can't even begin to describe how she will be missed in every layer of what goes on at the church."