The former Crusaders favourite sustained the injury in the Bulls' 38-4 Stobart Super League win at Widnes on Easter Monday.
"It's another blow to us just as we were looking at getting some players back," said Bradford football manager Stuart Duffy.
He continued: "Jarrod has been tremendous for us and there is no doubt he will be a big loss for the next couple of months.
"He has a similar injury to that suffered by Manase Manuokafoa earlier in the year and the prognosis of eight weeks is the same."
Sammut has been in excellent form for the Bulls this year and has a 79% success rate with the boot after taking over the goalkicking duties from the injured Luke Gale.
Bradford are doing it tough on and off the field, as they seek to raise the second half of the £1million they need to ensure the survival of the cash-strapped club.
Coach Mick Potter was without 11 members of his first-team squad on Monday because of injury and suspension and he will be without joint captain Heath L'Estrange for Sunday's Carnegie Challenge Cup tie against Doncaster.
The Australian hooker has entered an early-guilty plea after being charged with making a "spear" tackle on England captain Jamie Peacock during his side's 12-4 win over Leeds on Good Friday.
L'Estrange has accepted a two-match ban, which will also rule him out of the League clash with leaders Huddersfield on Sunday week.