The child was taken to Edinburgh's Sick Children's Hospital after he was injured at an address in the Hallglen area of Falkirk,
A spokeswoman for Central Scotland Police confirmed that the boy died late on Thursday afternoon.
She said inquiries were still at an early stage and were ongoing to establish the circumstances surrounding the incident.
She said no-one had been arrested or charged in connection with the incident on Tuesday.
She added: "A post-mortem examination is due to be carried out and we can't say any more until we know the results of that."
Neighbours of the boy's family said the child had been killed falling down the uncarpeted, concrete common stair in the three-storey council-built housing scheme block.
One resident described the toddler's death as "a terrible tragedy on our doorstep".
Another neighbour, Paul Nisbet, 30, said: "I saw the ambulance arrive, I saw the paramedics going in, and a wee while later coming out with the boy.
"One paramedic was holding him.
"I saw his mother at the back of the ambulance. She was distraught.
"I've been told he had fallen down the stairs – it's a terrible thing.
"His parents haven't been back to the flat since."
The boy's parents, who live up five flights of eight concrete steps, are said to have taken on a private rental of the property in November or December last year.