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.”
TVP added: “There is no indication that this incident is linked to the Black Lives Matter protest that took place in Reading today.”
Unconfirmed reports allege this is the perpetrator in the video.