It is alleged that the victim was attacked when he approached the youth outside the Renmore Barracks at around 10.45pm.
Mr Murphy, who was wearing civilian clothing at the time, ran through the barracks gate but was pursued by his attacker.
Army sentries fired five warning shots and used a baton to subdue the attacker until the Garda could arrive, the Defence Forces said, preventing the chaplain from suffering far worse injuries.
Mr Murphy thanked the public for their prayers in a post online on Friday, adding that he was awaiting surgery. “All will be well,” he wrote.
Taoiseach Simon Harris responded to the attack on Friday, saying his thoughts were with the member of the Defence Forces in hospital.
“I want to thank Defence Forces personnel and Garda for their action and response,” he added on X.
Micheál Martin, deputy defence minister and minister of defence, condemned the attack as he commended the sentries for their “critical” intervention.
“Our thoughts are with the Defence Forces member injured in the attack,” he added.
The Bidsophy of Galway, Michael Duignan, called the events “deeply shocking and upsetting”.
“I pray for the injured man, asking God that he would make a full recovery. I pray too for his family, for his army colleagues and for the medical personnel who are tending to his injuries at this time,” he said in a statement.