It happened in Hawbush Road at about 2.30pm on Monday.
West Midlands Police said the 17-year-old suffered an injury that was "not life-threatening" and an 18-year-old man has been arrested on suspicion of assault.
He remains in custody and is helping with inquiries.
Police have launched an appeal and anyone with information is being asked to come forward.
A spokesman for West Midlands Police said: "We’ve arrested a teenager on suspicion of assault following a stabbing on Hawbush Road, Brierley Hill, around 2.30pm on Monday.
"A 17-year-old boy was taken to hospital with a stab wound, thankfully his injury was not life-threatening.
"An 18-year-old man has been arrested and is in custody helping us with our enquiries.
"Violence among young people is a key priority for West Midlands Police and we continue to work with our violence reduction unit to understand the underlying causes and carry out preventative work with young people in schools, colleges and youth groups.
"Anyone with further information about this incident is urged to contact us via live chat on our website quoting 20/593459/22."
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org