Labyrinth (1986) and Pan's Labyrinth (2005) have a similar plot in that a young girl 'loses' her baby brother to 'monsters' and must get him back.
Is this based on some myth, fable, or legend from some culture?
Yes, in Greek mythology, the original labyrinth was built by Daedalus, on Crete, to keep the Minotaur (half man, half bull) imprisoned. This is likely where the idea comes from that labyrinths contain monsters.
King Minos, for whom Daedalus had made the structure, later had him imprisoned in the labyrinth instead, and this is whence his famous son Icarus fled using the wings made of feathers and wax his father crafted for him.
The archetype of the young girl could be based on Ariadne, the girl who fell in love with the hero Theseus, who was to kill the Minotaur and thus ventured into the maze. She gave Theseus a ball of string so he would be able to find his way back.
However, both Jim Henson and del Toro (the directors of Labyrinth and El Laberinto del Fauno [the better title], respectively) were influenced by many fairy tales and stories of young girls ending up in fantastical realms - Carroll's Alice in Wonderland in particular.
Ofelia shares her name with the Shakespearean character from Hamlet, but it has been pointed out that she has more in common with the titular character. 1
That Sarah Williams has to save her half-brother in Labyrinth was based on Maurice Sendak's Outside over There, but where the subplot of Ofelia bringing her baby half-brother into the labyrinth comes from is a little harder to pinpoint. Del Toro kept notes on what would become El Laberinto for over a decade, perfecting concepts for monsters and figuring out all the details, and the influences and personal inventions will make this extremely difficult to figure out.
Nevertheless, the narrative has a lot of (anti-)Catholic, mythical, and mystical undertones, and the sacrifice that Ofelia is asked to make towards the end could very well be a direct reference to the blood sacrifice made for the lives of others (but also the blood that necessarily needs to flow for new life to occur 2 ).
1: Pan's Labyrinth, A Critical Analysis by Safia Southey.
2: Many examples of this interpretation can be found online.