After coming fourth in the men's synchronised 10m platform diving event on Monday, the 18-year-old from Plymouth received a message telling him he had let down his father, Rob. Rob Daley died in May 2011 from brain cancer.
A 17-year-old boy was arrested at a guest house in the Weymouth area on suspicion of malicious communications. Dorset Police said they acted after being contacted by a member of the public at about 22:30 BST on Monday.
A spokesman was unable to confirm whether the arrest was specifically over the tweets to Daley or subsequent Twitter conversations with other users.
Daley responded to the tweet by posting: "After giving it my all...you get idiot's sending me this..." The user later posted a tweet apologising for the comment.
Source: BBC News