Police believe the youngster was deliberately targeted in the attack in a shop in Worcester and have released images of three men they want to speak to.
The boy was taken to hospital and is being treated for serious burns to his arm and face.
Worcester City Council leader Marc Bayliss said the attack was “absolutely pure evil”.
He added: “Worcester is not that sort of place. We are a quintessential small English city.
“I have never heard of an acid attack in Worcester so this is absolutely not something we have any experience of.”
He urged anyone with information to come forward, and added: “Think if this was a member of your family, an innocent child, a three-year-old probably scarred or damaged for life by this.
“We need to bring the perpetrators to justice, and quickly.”
The incident occurred at around 2.15pm on Saturday in the Home Bargains store on the Shrub Hill Retail Park in Tallow Hill.
A local shop worker, who did not want to be named, said he saw a number of emergency services at the store on Saturday and two police officers were stationed outside on Sunday.
“There were a couple of fire engines and a couple of police as well.
“Customers were still going in and then they completely shut up at about 3pm.”
Worcester MP Robin Walker described the attack as “horrific”, and added: “The shock will be universal, anyone conducting such an attack on a small child is just appalling.
“At this stage the key thing is for the police to act quickly and see if they can track down the perpetrator and understand what’s behind it because it is an unthinkable thing to happen.”
A 39-year-old man from Wolverhampton has been arrested on suspicion of conspiracy to commit grievous bodily harm and remains in police custody.
West Mercia Police said the three men in the photos may have “vital information”, and urged anyone who recognises them to come forward “as a matter of urgency”.
Chief Superintendent Mark Travis said: “At this time we are treating this as a deliberate attack on a three-year-old boy.
“The incident will rightly shock the local community and I would like to reassure local people that we are carrying out a thorough investigation to identify those responsible.
“At this time, the motive for the attack is unclear.”