The 16-year-old victim was walking in Bishopbriggs Park, East Dunbartonshire at around 7.30pm on Monday when he was approached by the two men, police said.
One threatened the boy with a knife and demanded his phone. He then stabbed him and the pair ran off with the mobile.
The boy was taken to Glasgow Royal Infirmary for treatment and was later released, Strathclyde Police said.
Both men were white and aged around 19-20. One was 5ft 9in and slim. He was wearing a grey hooded top and black woollen hat.
The other was wearing a dark-coloured tracksuit and had a dog on a lead.
They ran off in the direction of Kirkintilloch Road. Initial police inquiries have found that they may have been in Tofthill Avenue and Stirling Drive, Bishopbriggs after the robbery.
A spokesman said officers were carrying out door-to-door inquiries in these areas.
Detective Constable Steven Gault said: "This park is popular with the local community, with people out running and people walking their dogs. I am appealing to anyone who may have been in the park around the time of the incident to get in touch.
"If you have any information or knowledge, please do get in touch with us."