Daley's father died of brain cancer a year ago and the 18-year-old Olympian had hoped win a medal "for myself and my dad." But he finished fourth on Monday in the 10-meter synchronized platform with teammate Pete Waterfield.
Afterward, a Twitter user sent him several negative messages, including: "You let your dad down i hope you know that."
Dorset Police said early Tuesday that a 17-year-old man was arrested at a guest house in Weymouth "on suspicion of malicious communications" in relation to Twitter threats made against Daley.
In Britain, tweeting messages considered menacing can lead to prosecution.