The gaseous substance, thought to have been a type of pepper spray, was sprayed into the three nearby businesses in Upper Gornal on Tuesday evening and left one person needing hospital treatment.
Fourteen other people were treated for breathing difficulties but were discharged at the scene.
Police, paramedics, firefighters and specialist hazardous response teams were all called after the attack happened at around 7pm and the restaurants and supermarket were closed in the aftermath.
All three businesses are on Kent Street, with McDonald's around 50 metres down from Tesco and Pizza Hut which are set back from the main road at The Arcade.
They were all closed on Tuesday evening and forensic specialists have examined each business with the nature of the substance believed to be a type of pepper spray.
A man later handed himself into police at Brierley Hill police station on Wednesday with the 20-year-old now being questioned by the force.
Tesco and McDonald's were both back open as normal on Wednesday morning after being deep cleaned overnight.
A West Midlands Police spokesman said: "Following fast-track CCTV enquiries, detectives made several attempts to locate a suspect and the 20-year-old is currently in custody for questioning on suspicion of administering a noxious substance.
"Anyone with any further information should contact us via Live Chat at west-midlands.police.uk between 8am and midnight or call 101 anytime quoting log 4401 of 20/10."
A total of 10 firefighters and two fire engines from West Midlands Fire Service were sent to the scene after being alerted by police.
A spokesman for the fire service said: "It is believed that someone had released a substance, which resulted in a number of people being assessed and treated by West Midlands Ambulance Service.
"Two of our crews attended – two fire engines and ten firefighters, from Tipton and Dudley fire stations. Specialist officers from our Detection, Identification and Monitoring team assessed the scene and declared it safe."
Meanwhile West Midlands Ambulance Service sent an ambulance and two paramedic officers along with the Hazardous Area Response Team. Paramedics were initially called to Pizza Hut but were soon also needed at Tesco and McDonald's.
A spokesman for the service said: "In total, 15 patients self-presented to our members of staff, 14 of whom were discharged at the scene.
"One patient, a man, was treated for symptoms at the scene before being taken to Russells Hall Hospital for further assessment."
A spokesman for Tesco said: "Our Dudley Gornal Express was closed temporarily last night after an incident at The Arcade in Upper Gornal.
"The store is now open again after being deep cleaned overnight and we are helping the police and fire service with their investigation."
A spokesman for Pizza Hut Delivery added: "We are working with our team members to ensure their well-being and have been informed none of our staff or customers have been injured.
"We are cooperating with relevant authorities at this time."
A spokesman for McDonald's said: "Following an incident last night impacting both our Upper Gornal restaurant and a number of other local businesses, the restaurant was temporarily closed and all of the team were offered support.
"Following an extensive clean, it reopened as usual at 6am this morning. We continue to assist the police with their investigation."