The incident happened at around 4pm yesterday (Monday, January 7) in the Regent Street area of Leeds.
West Yorkshire Police confirmed on Tuesday morning that enquiries were still ongoing in relation to the second male.
A West Yorkshire Police spokeswoman said: "Police are investigating an affray involving two males which is reported to have occurred in the Regent Street area of Leeds at around 4pm this afternoon (Monday, 7 January).
"A 16-year-old boy has been arrested and is currently at hospital receiving treatment for a non-life threatening stab wound.
"Enquiries are ongoing to trace another male who is believed to have been involved."
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