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.
Detective Chief Superintendent Ian Hunter, from Thames Valley Police, said police are not looking for any other people in connection with the attack.
He added: “This is not currently being treated as a terrorism incident, however officers are keeping an open mind as to the motivation for the incident and are being supported by colleagues from Counter Terrorism Policing South East.”
Police have asked anyone with mobile phone footage of the attack to come forward.
But people have been urged not to share videos and photos online “out of respect for the victims’ families” after footage was circulated on social media.
Thames Valley Police said the incident was not connected to an earlier Black Lives Matter (BLM) protest in the park.
About a dozen armed police officers carrying shields were later seen entering a block of flats in Basingstoke Road in Reading at around 23:00 BST. (Courtesy BBC)