The teenager, from Langton Matravers, was staying in Swanage when she disappeared on 7 November.
Searches took place at two addresses in Swanage and the man and woman were arrested.
Police said they were both known to Gaia.
The last reported sighting of the teenager was at an address in Manor Gardens on Morrison Road on 7 November.
She was said to be wearing a red checked shirt with white buttons, grey and white woven leggings and white trainers and she went missing without her medication.