The 28-year-old defender, who completed his signing from Burnley alongside Clarets team-mate Chris Eagles on Friday, will now miss several months of the new season.
Manager Owen Coyle told the club's official website: "Ty went in for a challenge and unfortunately suffered the injury.
"It was desperately unlucky for him and we will make sure that he is fully supported in his rehabilitation.
"He will go for a check and an assessment in a month and that will indicate more accurately the timescale for his recovery."
Mears, who was pencilled in to take the right-back slot for Wanderers this season, has instead become the club's third long-term absentee and second player to break his leg in pre-season.
The Trotters' 2010/11 player of the year Stuart Holden suffered anterior cruciate ligament damage in March and fellow midfielder Lee Chung-yong was ruled out for a minimum of nine months after breaking his right leg in a friendly against Newport.
Gretar Steinsson and Sam Ricketts are available to provide cover for Mears, but boss Owen Coyle may be persuaded to add to his squad after losing another first-teamer.