The Italian boy fell more than ten metres when the door of the lift at Furio Camillio stop, on Line A, opened and he stepped in without see that the lift wasn't there, Ansa reported.
The tragedy was seen by his mother and a metro worker, who are being treated for shock.
An officer from Atac, Rome's transport department, has been detained along with two others.
Rome Transport Councillor Guido Improta said on Thursday that the accident was probably down to “human error”.
“The station agent carried out a procedure he shouldn't have, perhaps because conditions were difficult, and in the end there was the tragedy,” he was quoted by Ansa as saying, adding that the lift was “blocked” at the time.
Rome mayor Ignazio Marino met the child's parents at the scene, telling them he would declare a day of mourning on the day of the boy's funeral.
But he was reportedly heckled by bystanders, who told him to “go away”.