Rockingham County (N.H.) Attorney Jim Reams told the Boston Herald by phone the Plaistow couple, Jessica Linscott, 23, and her boyfriend, Roland Dow, 27, were apprehended about 6 p.m. in Orlando.
The Boston Globe reported Plaistow police and the U.S. Marshal's Service said the pair were standing in line at an unidentified amusement park when taken into custody.
"We knew we would get them, it was just a matter of when," the Herald quoted Reams as saying, adding it was a joint effort with Plaistow, Florida and federal authorities. "Ultimately it was tips that helped track them down. I know it was a tip in Florida."
Linscott and Dow are to have a court appearance Thursday and authorities intend to have them extradited to New Hampshire.
Linscott's son had a badly burned wrist and fingers and a severely battered skull when he was dropped off at a hospital in New Hampshire early this month.
Dow, who allegedly beat the boy Nov. 1, is facing first and second-degree assault charges, while Linscott is charged with endangering the welfare of a child and neglect.