Her unattended golf bag was discovered by golfers at the Coldwater Golf Links in Ames early on Monday, and police found her body in a pond a short distance away with stab wounds to the head, neck and upper torso.
The suspect, Collin Daniel Richards, was charged with first-degree murder and appeared in court on Tuesday.
"Our thoughts and prayers go out to the family and friends of Celia Barquin Arozamena," an Ames Police Department spokesman told a news conference on Tuesday.
"During a search of the wooded area next to the golf course, officers located a subject who spoke of another individual living in the wooded area who had made statements of having an urge to rape and kill women."
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A police dog tracked the scent from the victim's body to a location in the wooded area, where police encountered Richards, who had "fresh scratches on his face consistent with a fight and was attempting to conceal a laceration on his left hand."
A knife and clothes covered in blood were also recovered, and Richards was charged with first-degree murder, the spokesman added.
Story County Attorney Jessica Reynolds told the Des Moines Register newspaper that the state believed Richards to be a "flight risk" and "a danger to the community."
Tributes poured in for Barquin, with Iowa State's head women's golf coach, Christie Martens telling local media the young golfer was a "beautiful person who was loved by all her team mates and friends."
Spain's sports minister Jose Guirao tweeted that "her loss leaves us broken" and offered his condolences to her friends, family and "the whole family of sports."
(Reporting by Simon Jennings in Bengaluru; Editing by Hugh Lawson)
