Reading stabbings: Three feared dead in suspected terror attack
At least two people are being treated for knife wounds in hospital, while a source said there had been three fatalities - but this has not been confirmed by emergency services.
The attack took place at around 7pm in Forbury Gardens in the town centre - and a man was arrested at the scene and taken into police custody, Thames Valley Police (TVP) said.
The security source added that the man who has been arrested is Libyan.
Personal trainer Lawrence Wort, 20, who said he was around 10 metres from the attack, told PA: "The park was pretty full, a lot of people sat around drinking with friends, when one lone person walked through, suddenly shouted some unintelligible words and went around a large group of around 10, trying to stab them.
"He stabbed three of them, severely in the neck, and under the arms, and then turned and started running towards me, and we turned and started running.
"When he realised that he couldn't catch us, he tried to stab another group sat down, he got one person in the back of the neck and then when he realised everyone was starting to run, he ran out the park."
The two casualties are being treated in the emergency department of the Royal Berkshire Hospital, a spokeswoman said.
Prime Minister Boris Johnson tweeted: "My thoughts are with all of those affected by the appalling incident in Reading and my thanks to the emergency services on the scene."
Home Secretary Priti Patel tweeted that she was "deeply concerned" and it is understood she is being kept updated on the situation.
A Thames Valley Police statement said:"A number of people sustained injuries and were taken to hospital.
"A police cordon is in place in Forbury Gardens as officers investigate. We are asking the public to avoid the area at this time."
Two air ambulances and several police vehicles responded to the attack, with images on social media showing a significant police presence.