A 25-year-old man from Reading has been arrested on suspicion of murder after being detained at the scene.
The attack happened at Forbury Gardens at about 19:00 BST where several people were stabbed.
Police are not currently treating the incident as terror-related, but counter terrorism officers were called.
Security sources have told the BBC a man arrested at the scene is thought to be Libyan.
One eyewitness told the BBC how he saw a man move between groups of people in the park trying to stab them and how the man ran towards him.
There were reports a police officer had "rugby tackled" the suspect to the ground, according to the Sunday Mirror.