The 21-year-old, who joined from Arsenal last week, lasted just 20 minutes of his debut against Southend on Saturday before sustaining the injury, and X-rays have shown a fracture.
However Moore, who concedes the absence will be a massive blow, has been given the green light to bring in a replacement.
"He has broken his collarbone so that is going to be six to eight weeks. It's the way things are going for us at the minute," Moore said.
"The pleasing thing for me is I told the chairman and he has said to go out and get another ball-playing midfielder. Whether we will be able to go out and pull another Arsenal player out of the bag again, we'll have to wait and see.
"Randall will stay with us but he's going to have to go back there for treatment. It's a massive blow for the lad."