Laundrie, the only person of interest in his girlfriend Gabby Petito's death, remains wanted for bank fraud.
The 22-year-old's remains were found in Wyoming late last month.
Sims was found in a hospital in good condition, authorities said.
He's been sought for questioning since fiancée Gabby Petito was reported missing and was later found dead in Wyoming.
Cassie Laundrie said she hadn't "been able to talk to" her missing brother.
The 19-year-old disappeared in Orlando last Friday. A person of interest in the case was found dead earlier this week.
The Laundrie family attorney says the three of them camped Sept. 6-7, shortly before Gabby Petito's family reported her missing.
"Look to yourselves on why that’s not being done,” Joe Petito urged members of the media.
Armando Manuel Caballero was seen entering the 19-year-old's apartment shortly before she went missing.
The 24-year-old's clothes, phone and wallet were in his crashed car, which was found abandoned on its side in rough desert terrain.