Costello, who was yet to feature for the Giants first team, was airlifted to Leeds General Infirmary following the incident during an under-19s match against Salford.
"It is with regret that Huddersfield Giants wish to inform everyone of the passing of 17-year-old academy player Ronan Costello," a statement from the club said.
"The club have been asked by the family to send their thanks for the messages of support they have received to date and have requested that all well-wishers now allow them to grieve and respect their privacy.
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"The Huddersfield Giants are collating all messages, cards and tweets that they receive to pass to the family at the appropriate time."
In a statement the family said: "We are absolutely devastated to lose Ronan so tragically and suddenly.
"Ronan was a loving and caring 17-year-old lad who was dedicated to his family and friends. He was a credit to all of his family and we are so proud of him and his achievements.
"We are all truly heartbroken and Ronan will be missed and forever in our hearts."
A Daily Mail report claimed Costello suffered a head injury, but the club has not confirmed this.
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