Positive Action in Housing said that Health Secretary Alex Neil MSP had written to them to say that medics were happy to treat three-month-old Mohammad Sudais in Scotland.
The Afghan boy suffered third-degree burns after a gas explosion in his parents' home in Peshawar seven weeks ago.
His father Mohammad Ameen, 30, mother Sumaira, 28, and 13-month-old brother Abdul Haseeb were killed in the explosion. Doctors in Pakistan had said that they could do no more for the little boy.
They recommended the best place that he could be treated properly was in Glasgow Royal Infirmary, in the city where his uncle, Mohammad Asif, lives.
Positive Action in Housing launched an appeal on Thursday to raise £15,000 towards the cost of bringing the baby to Scotland and has raised £6906 so far.
Mr Neil said: "We are very happy to treat baby Mohammad in Scotland and we are working hard with all the relevant agencies, including the UK Government, to make sure that happens."
Mr Asif, general secretary of the Scottish Afghan Society, welcomed the news, though he was still waiting for details about when his nephew could actually be brought to Scotland.
He said he was very grateful to the Scottish people for raising funds and welcomed the help of the Scottish Government and Mr Neil