The nine-year-old was discovered in the base of a bed at a flat in the area after police smashed their way in on Friday.
Police said the schoolgirl had spent a "comfortable and settled night and is starting on the road to recovery following her ordeal".
She spent the night watching DVDs and has been playing with a kitten.
Matthews had been missing for nearly four weeks, sparking a massive police search which involved about 10 percent of the West Yorkshire police force.
Detectives said they will begin to talk to Matthews, who is the subject of an emergency police protection order, following medical checks.
"The interviews may be a long process but throughout this enquiry our main focus has been and continues to be Shannon's welfare," police said in a statement.
The order will remain in place until police have "had time to establish the full facts of what happened in the time since her disappearance".
Matthews was found after detectives broke down the door of the house a mile from her family home in Dewsbury.
Neighbours said the girl appeared "quite calm" when she emerged from the house in Batley Carr.
A 39-year-old man was arrested on suspicion of abduction.
Her father, Leon Rose, told Sky News that finding her was "like winning the lottery".
Locals were later pictured ripping up "Missing Shannon" posters and throwing them in the air like confetti in celebration of her safe return.
Matthews had gone missing on February 19 after a swimming trip, prompting one of the biggest investigations in the area since the Yorkshire Ripper inquiry of the late 1970s.
