The teenager was arrested on suspicion of causing grievous bodily harm and possession of a bladed article.
The man was arrested of possession of a bladed article.
Police were called to the cinema complex at 8.15pm on Sunday to reports of a fight.
A 20-year-old man was taken to hospital with non life-threatening injuries. He was later released from care.
“Our officers have acted quickly to establish the circumstances around this incident leading to two arrests and the recovery of a knife,” said Superintendent Ross Cooke of Nottinghamshire Police.
“Isolated incidents such as this are incredibly serious and as a force we are committed to ensuring that appropriate action is taken to keep people safe and bring to justice those responsible.”
Those who witnessed the incident or have information about it are asked to contact the force on 101 and quote incident number 804 of 1 December 2019.