Paramedics were called to The Mitre pub, on Spider Island, in Allenton, at about 15:00 GMT on Sunday.
The 24-year-old man was arrested in the early hours of Monday and is in police custody. The teenager remains in a serious condition in hospital.
"We would urge anyone who might have information that could help us to come forward immediately," police said.
A man has been arrested on suspicion of attempted murder after a 16-year-old boy was stabbed outside a pub in Derby.