Emergency services were called to Forbury Gardens in the town at about 19:00 BST on Saturday.
Two air ambulances were photographed landing at another park nearby to ferry the injured to hospital.
Armed police officers raided a block of flats in the town hours after the attack and large parts of the town remain cordoned off.
A 25-year-old man from the town, arrested on suspicion of murder on Saturday, has been now been re-arrested under Section 41 of the Terrorism Act 2000, Counter Terrorism Policing South East said.