Emergency services were called to Sandown Court in Avenham shortly before 8am on Friday, after a 25-year-old woman suffered serious injuries after falling from an 8th floor apartment.
She was taken by ambulance to the Royal Preston Hospital where her condition was described as critical.
The incident is currently being treated as unexplained, and police have launched an investigation.
A 29-year-old man from Preston has been arrested on suspicion of attempted murder and was in custody on Friday.
Extra police patrols were in the area to act as reassurance.
Enquiries are continuing.