Gwent Police was called to Cardiff Road at about 17:45 BST on Thursday.
A 61-year-old man has been taken to Cardiff's University Hospital of Wales with life-threatening injuries. A 43-year-old man is being held in custody.
Insp Jason White said: "We are fully committed to establishing all the circumstances surrounding what happened this evening."
A man has been arrested on suspicion of attempted murder following a stabbing in Caerphilly town centre.