Bresnan injured his left Achilles during the Champion County match against MCC in Abu Dhabi earlier this month.
The prognosis was initially encouraging, but the problem is worse than feared and the club are awaiting the outcome of a scan.
Yorkshire captain Andrew Gale said: “He had a scan which doesn’t look that great.
“We aren’t sure how long he will be out, but I don’t think he will start the season, which is a bit of a blow. But I guess if you would want to miss him, it would be at the start because we’ll have a lot of the England players coming back.
“He bowled beautifully on tour; he missed the T20s because he didn’t feel quite right, but the first innings of the MCC game he got four-for and showed what good skills he has on flat pitches.”
Bresnan, 31, was ever-present in last year’s Championship and played a key role as Yorkshire retained the title, scoring 849 runs at 49.94 and taking 45 wickets at 30.88.
Yorkshire have plenty of seam bowling options, however, with the likes of Ryan Sidebottom, Jack Brooks, Steve Patterson, Liam Plunkett, Matthew Fisher and David Willey.
Yorkshire start their Championship programme against Hampshire at Headingley on April 17.