The man, 22, was taken to hospital after being splashed with the liquid, which is thought to have been an alkali.
Police were called to the Christmas market in the central London park at about 20:00 GMT on Sunday, following reports of a fight between two groups of people.
Two men, aged 21 and 18, remain in custody on suspicion of causing grievous bodily harm, while a boy aged 16 has been released on bail until February.