Emergency services rushed to Silver Jubilee Park, on Oak Street, at around 6pm on Thursday and found a 15-year-old with the injury.
The teenage boy was taken to hospital but his injuries were not thought to be serious, a spokesman for West Midlands Police confirmed.
The 14-year-old was arrested on suspicion of wounding and remained in custody for questioning as of Friday afternoon, the force said.
An ambulance, a MERIT trauma doctor and critical care paramedic attended the scene. The 15-year-old was given trauma care on scene before being taken to hospital.
Meanwhile enquiries around exactly how the teenager sustained his injuries are ongoing and people with any information are asked to contact police.
Anyone with information can contact the force via Live Chat on their website and quote 20/622430/22.