Brooks has injured his left calf in a blow on the eve of the new county season.
Fellow pace bowlers Ryan Sidebottom (tight hamstring) and Liam Plunkett (tight calf) are also nursing niggles.
The Championship campaign starts in 10 days when Yorkshire take on Hampshire at Headingley.
“Jack Brooks has unfortunately picked up a calf injury,” confirmed first-team coach Andrew Gale.
“We’re looking at four to six weeks depending on how quickly he recovers.
“Ryan Sidebottom’s got a tight hamstring, so we’re unsure how long that’s going to be at this stage.
“Liam Plunkett has got a slight calf problem.”
Brooks, 32, could miss up to three Championship and five One-Day Cup matches.
He has been Yorkshire’s leading wicket-taker in each of the last three seasons, taking 60 Championship wickets last year, 65 in 2015 and 68 in 2014.
Along with Sidebottom, Brooks spearheads the Yorkshire attack and is vital to the club’s hopes of reclaiming the Championship.
He is also an increasingly useful lower-order batsman; last year he chipped in with 250 runs at an average of 27.
“It’s frustrating,” added Gale. “We specifically put a plan in place for him, as he had a calf injury in January (a different one) and came back from that.
“So we sent the bowlers out early (on the pre-season tour) and now they’ve got injured. What can you do?”
Neither Brooks nor Sidebottom have played on the trip.
Plunkett is returning to the squad’s base in Dubai for assessment after his calf problem flared up in the ongoing MCC versus Middlesex Champion County match in Abu Dhabi.
Yorkshire have played a couple of two-day games on the tour, against the slightly incongruous opposition combination of Papua New Guinea and Lancashire.
They end their programme with one-day matches against Papua New Guinea tomorrow and against UAE Blues on Thursday before returning to England for their opening first-class game, a three-day affair against Leeds-Bradford MCCU starting at Headingley on Sunday.
Despite the injury concerns affecting his squad, Gale pronounced himself pleased with Yorkshire’s efforts yesterday on the second day of the Lancashire fixture.
After Yorkshire had scored 235-7 on the first day, Jack Leaning making 48 and Gary Ballance 40, Lancashire replied with 240-7, Karl Brown striking 74 and Steven Croft 70.
There were two wickets apiece for pace bowler Ben Coad and spinner Azeem Rafiq as Yorkshire’s inexperienced attack turned in an encouraging display.
Reflecting on his team’s performance overall, Gale said: “I think after the last game we wanted to up the intensity a little bit, and that’s exactly what we did.
“From a batting point of view the positives were that a few guys spent quite a bit of time at the crease.
“However, we would have liked one or two to go on and make a big partnership or score some hundreds.
“From a bowling point of view, I thought we were outstanding.
“I thought we controlled the run-rate all day and put the ball in good areas.
“If you’re going to be successful in the First Division (of the Championship), that’s what you’ve got to do.
“We have got a few injuries at the moment, so there are going to be opportunities for players.”
One man particularly keen to grasp his opportunity to impress Gale is Matthew Fisher, the 19-year-old pace bowler.
Fisher bowled six overs on his return to action after a frustrating year with injury, although he is not expected to be ready for first-team cricket straight away.
“It was good to get out in the dirt,” said Fisher, who returned tidy figures of 0-14.
“I had a tough summer last year, so it’s been nice to be out with the Yorkshire lads and get with the banter again.
“It was a tough first few days of the tour, but, as you get into it, your body gets used to it.
“It felt good (on Monday), and I’m really happy.”
Fisher, who has had a testing time with hamstring problems, added: “I wasn’t planning on playing this game, but, because I’ve been going quite well in the nets, I’ve been kind of thrown into it.
“We bowled beautifully, and the lads look to be grooving where they want to be on the pitch.
“I’m fit to play and do what I did, but I reckon it’s two or three weeks off me being fully confident that I could get through a day and bowl 15 overs.”