The boys – two aged 15 and one aged 17 – are in custody being questioned on suspicion of murder, Thames Valley Police said.
The victim, 15, was attacked in Salt Hill Park at about 6.30pm on Saturday following an argument with a group of males.
Officers believe those involved knew each other and that the attack was not random.
The boy was pronounced dead at the scene but has not been formally identified.
His family have been informed.
A post-mortem took place on Sunday afternoon, which concluded that the boy died from a stab wound to the chest.
Detective Chief Inspector Andy Shearwood, of the Thames Valley Police Major Crime Unit, said: “We have now made three arrests as our murder investigation progresses.
“A scene watch which has been in place at Salt Hill Park will soon be lifted and the park will be reopened to the public as soon as possible. Thank you to everyone for their patience throughout this.”
Anyone with information is asked to call police on 101 quoting reference number 1240 12/9. Or they can contact Crimestoppers anonymously on 0800 555 111.