The goalkeeper is one of the many Chelsea youth products who are out on loan, and has spent this season with Championship outfit Leeds.
Blackman is yet to make an appearance for the Yorkshire side in the eague so far this season, and suffered his injury while playing for the club's U-23 side against Birmingham.
As a result of the injury, he was stretchered off the pitch and went to hospital where he was treated for a broken tibia.
"Jamal would like to thank the medical staff at both Thorp Arch and Leeds General Infirmary for the excellent way they dealt with the situation and also expressed his thanks to supporters for their kind messages of support," a statement on Leeds' website said.
"Everyone at Leeds United wishes Jamal a quick recovery."