The children, along with five guardians, arrived by military plane at Scholes airport in Galveston at 4:40 a.m. Thursday.
They are now at the hospital's pediatric burn center.
Within 24 hours of the first eruption over the weekend, Shriners says an emergency medical team from its Galveston hospital was sent to provide care in Guatemala, where they've been working for days.
Doctors at Shriners Hospital said in a press conference that the children received thermal burns from ash clouds.
The six children who were selected to receive care in Galveston were chosen because, although they have severe injuries, they can be treated.
However, doctors say the healing process will take years. Four of the kids are on ventilators. Doctors were able to talk to two of the patients.
The exact ages of the children have not been released due to medical confidentiality, but we do know they are between the ages of one and 16 years old.
At Galveston airport, @GalvestonSHC medical staff and #Shriners have been waiting for 6 badly burned children from #Guatemala to arrive. Military plane just landed. They’ll be loaded into ambulances soon. #abc13 #breaking pic.twitter.com/IMyHNaccPq— Courtney Fischer (@CourtneyABC13) June 7, 2018
"We have some of the world's leading doctors. They go all over the world. Not just here. All over the world. Teaching other doctors how to treat burn patients. We're very proud of them," said Raymond Rubio with the Galveston Shriners.
The children are receiving free care from the Shriners, who provide on-site housing for their families.
According to the doctors, care will cost over $1 million per patient. When the children and their families are able to return home to Guatemala, Shriners doctors will fly with them to check in.
"It's very important that we support these children. They suffer severe burns. Back in the early days when we were doing this, a severely burned child had about a 35 percent chance of survival. Now, it's up to nearly 90 percent. They perform miracles everyday at our hospital here," Rubio added.
Each patient is described as having "massive burns" on more than 15 percent of their bodies.
Anyone who is interested can contribute toward the recovery efforts by donating online.
You can also call 855-393-7447 to make a donation.
Here in Houston, some volunteers are accepting donations at area restaurants for those affected by the volcano.
You can drop off non-perishable items to Guatemala Restaurant at 3330 Hillcroft St. Houston, TX 77057.