Breaks to his tibia and fibula occurred while the Marc VDS Honda rider was training at the Bellpuig motocross track in Spain.
Dr Eugenio Gimeno operated on Miller to insert compression plates and screws to the two fractures.
The Townsville-born 21-year-old will remain in Hospital University Quiron Dexeus for at least two days.
His recovery is expected to be closely monitored before a decision is made whether he will be fit to ride at the first MotoGP pre-season test at Sepang on February 1.
“Jack was unfortunate to sustain an injury so close to the start of pre-season testing, but riders need to train and there is always some risk when you train on the MX bike,” team principal Michael Bartholemy said.
“The good news is that the injury is not quite as severe as we first thought and that the surgery was successful.
“For a normal person the recovery period after such an injury would be long, but racers aren't normal people and I'm sure Jack is keen to get back on a bike as soon as possible.
“What is important now is that we monitor his recovery and that he rides again only when he is fit enough to do so, even if that means him missing the first of the MotoGP pre-season tests in Sepang.”
Miller undertook a difficult maiden year in the MotoGP class last season after stepping up from the Moto3 ranks.