The fight broke out at about 8.50pm yesterday (Wednesday), outside a shop at the junction of Dorset Road and Sandhurst Road, Harehills.
Officers had received reports of "a large number of people fighting, some armed with sticks and metal bars," according to a spokesman for West Yorkshire Police.
Detectives today said the fighting appeared to come after a "business dispute".
One man suffered a suspected broken hand and was taken to hospital, while another had a serious cut to his head that required stitches. A Mercedes car was also damaged.
Police arrested seven men yesterday on suspicion of violent disorder, in connection with the brawl, the force spokesman said.
Detective Inspector Phil Jackson, of Leeds District CID, said: “Our investigation is at an early stage but it appears this incident has come about as a result of business dispute.“Officers were on the scene very quickly and the situation was brought to a safe conclusion. A large crowd had gathered to watch what was happening and we are aware that footage of the incident has been posted to social media."
Det Insp Jackson said police CCTV cameras also picked up the brawl, but appealed for anyone with phone camera footage to get in touch.
He added: “Violent incidents such as this cannot and will not be tolerated and I’m sure the majority of those in the community will support our efforts to identify those involved.
“We are working closely with our colleagues in the local neighbourhood policing team who have increased their patrols of the area to reassure the community following this incident.”Anyone with information is asked to contact Leeds District CID via 101, quoting crime reference 13180326930. People can also call the independent charity Crimestoppers anonymously on 0800 555 111.