Staggs left the field in the first half of the 30-14 trial win over Canterbury on Saturday and did not return.
Brisbane medicos thought Staggs would be OK but he pulled up sore on Monday with scans revealing an issue.
"Kotoni will spend the next four to six weeks with our rehab staff," Broncos head of performance Dave Ballard said on Tuesday.
"We know he'll be doing everything he can to get back on the paddock and has already begun that rehab program today."
The Broncos said halfback Jock Madden had also picked up a hamstring injury in the Bulldogs clash and won't be available for round one.
The club also confirmed in a statement star prop Payne Haas (ankle) was on track for the round-one clash with Sydney Roosters.
Haas, who had an ankle cleanout in pre-season, came off in the first half against Canterbury with what the club said was "an orthotics issue" in his shoes.
Second-rower Jack Gosiewski was concussed against the Bulldogs and must undergo the 11-day recovery protocol to play in the March 6 clash with the Roosters.
The absence of Staggs will open the door for last year's leading try scorer Deine Mariner to force his way into the starting side.
Mariner was overlooked in the starting lineup against the Bulldogs with coach Michael Maguire preferring Gehamat Shibasaki, but now his inclusion looms as an obvious choice.
Veteran Delouise Hoeter is another option for Maguire at centre.
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