The division bench headed by Justice P V Hardas asked the Joint Commissioner of Police (Crime) to assign the case to a senior officer of the Crime Branch, unit 4.
The case was earlier being probed by Bhoiwada police.
The child went missing from the hospital on October 25, 2012, from the maternity ward when his mother, Jasmin Devdas Naik, was away.
Eye witnesses said that an unknown woman was seen leaving the ward with the boy in her arms.
Police told the court that despite best efforts, the child as well as the woman remained untraceable.
The High Court today observed that this was a serious matter and local police had enough opportunity to find the child, but they failed, hence the court had no other option but to transfer the case to the Crime Branch.