Officers were called to a takeaway in St John's Road, Birkby, after reports shots had been fired at about 10.30pm on August 23.
Staff and customers were in the shop at the time, and a 19-year-old man was taken to hospital for treatment for a minor injury caused by broken glass.
Today West Yorkshire Police said a 21-year-old man has now been arrested on suspicion of attempted murder following the incident.
He remains in police custody.
The force is also appealing for anyone who saw a blue Seat Leon driving in the area at the time of the incident to come forward.
Detective Inspector Andy Farrell, of the force's Firearms Prevent Team, said: “We are still exploring the wider circumstances surrounding the incident and we are continuing to appeal for anyone with information to contact officers.
“We believe this was a targeted attack involving parties known to each other, and thankfully no one was more seriously injured in this incident.
“The criminal use of firearms on our streets is something we will always take extremely seriously and we have specialist officers and firearms officers continuing to carry out extensive enquiries.
“I would urge anyone who has any information on the incident to contact police on 101. I would especially like to hear from anyone who witnessed a blue Seat Leon driving in the area at the time of the incident.
“Neighbourhood patrols continue to be carried out in the area to offer extra reassurance to the community.”
Anyone with information is asked to contact police on 101, quoting crime reference 13180421039 or to use the live chat facility at www.westyorkshire.police.uk
Information can also be passed anonymously to independent charity Crimestoppers on 0800 555 111.