Crews from Chichester and Bognor attended the scene at 5am after they received reports of smoke billowing from the first floor of a two-storey flat.
A female was rescued by the fire crews and given oxygen before being checked by paramedics.
Fire crews left the scene just after 6am.
A spokesman for West Sussex Police said: “Just after 5am, a fire started in a small apartment in Pagham.
“A 22-year-old female has been arrested in connection with the incident.
“Police are continuing with the investigation.
“Anyone with any information should contact police officer Hughes, quoting reference number 0269 16/11/13.”