Courtney Sheward, 33, was being held Thursday night on $25,000 bail.
Her teenage son was a member of the same troop as the scout she is accused of having sex with, police said.
"It was through her involvement as a volunteer parent that she met the 16-year-old male victim and a relationship began," said Fort Worth police Sgt. Chad Mahaffey. "As a result of the relationship, they had nonforcible sex."
Police said even though the sex wasn't forced, she was charged with sexual assault because the victim is younger than 17 and is considered a juvenile.
Detectives are investigating allegations involving at least one other boy, police said.
"The arrest of Mrs. Shewar was based upon legal sufficient proof that she had sex with someone under 17 years of age," Mahaffey said. "However, our investigation is continuing into the possibility and likelihood of other victims."
An executive with the Scout's Longhorn Council, which includes Tarrant County, said the group was shocked at the arrest.
"Obviously, we're deeply outraged by the actions, and we feel for the families," said Dan Clifton, chief executive officer of the Longhorn Council. "We're waiting for the outcome of the investigation."
Sheward was a member of a committee that oversaw the troop and helped plan activities and keep records, Clifton said.
She was removed from the position on Tuesday as soon as the scouts learned of the allegations, he said.