Officers believe he was deliberately targeted in the attack in Worcester on Saturday and have released images of three men they would like to speak to.
-> Three generations of West Yorkshire family injured in head-on smashThe boy was taken to hospital where he is being treated for serious burns to his arm and face.
West Mercia Police has appealed for anyone with information about the incident, which occurred around 2.15pm in the Home Bargains store on the Shrub Hill Retail Park in Tallow Hill, to come forward.
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.
-> Police helictoper apologises for noise over Leeds after apprehending two burglars"Officers are working hard to establish exactly what happened and what the substance involved was.
"The three men in the photo may have information vital to our investigation.
"I am sure someone will recognise them and I would urge anyone with information to contact us as a matter of urgency."
A 39-year-old man from Wolverhampton has been arrested on suspicion of conspiracy to commit grievous bodily harm and remains in police custody.