Ellen Higginbottom died after being brutally attacked near Winstanley College, and her body was discovered at Orrell Water Park in the early hours of Saturday morning.
A post-mortem examination has concluded that the 18-year-old student had suffered multiple wounds to the neck.
Greater Manchester Police says the suspect was detained on Sunday afternoon in nearby Billinge, and is currently in custody for questioning.
Detective Superintendent Howard Millington has stressed the investigation "is still in its early stages".
He said: "This investigation is by no means over however, we still have a long way to go in piecing together the puzzle.
"Our investigative team will continue to work at the scene in the area around Orrell Water Park for the next few days."
Classmates have described Ellen as a "lovely and caring girl" who will be remembered for her love of horses.
Her friend Katie Hatton wrote on Facebook: "Absolutely heartbreaking that this horror had to happen to such a lovely and caring young girl, always smiling and making me laugh in psychology.
"You were taken far too young - my love and thoughts are with friends and family. R.I.P. Ellen."
Lisa Wasilewski wrote: "Seriously saddened by the loss of the lovely Ellen Higginbottom. My thoughts are with her family right now.
"I will always remember you for your love of horses and your bubbly personality. You will be missed xxx."
Chloe Williams, who had posted a plea for information about Ellen in the hours after she went missing, said later: "Never felt as sick and upset and heartbroken in my entire life."
Winstanley College released a statement saying the community was "shocked and mourning the loss of a wonderful young woman".
It said it was helping affected students "come to terms with something no one should ever have to come to terms with", adding: "Please be kind to each other and take care."
The headteacher of nearby Lathom High School, Jane Galbraith, tweeted: "All of us @LathomHS are thinking of you all at this terrible time."
Ellen had been reported missing by her family at 7.20pm on Friday evening when she failed to return home from college. They said her disappearance was very out of character. Receive Instant News Update Via BBM: D3EDEFDF...Click HERE for Details. Share your story with us: firstname.lastname@example.org PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How I TOTALLY Got Rid Of my POT BELLY,excess Fat and Overweight In just 2weeks.. Click HERE for Details. Warning To Men: This 3 Foods Is Killing Your Erection. Click Here To Know Them