The injury reportedly occurred while he was lifting in the weight room.
Despite the missed time, Fann reported the team is optimistic he will be able to return in time for training camp.
Breida was a breakout star for the 49ers last season after presumptive starter Jerick McKinnon missed the entire season with a torn ACL.
Although injuries limited him at times during the season, the former undrafted free agent appeared in 14 games and led the team with 814 rushing yards and three rushing touchdowns. Only tight end George Kittle had more than Breida's 1,075 yards from scrimmage.
The 24-year-old also averaged 5.3 yards per carry, good for fourth-most in the NFL.
While he was likely looking at a significant role in 2019, he will not only have to compete with McKinnon but also Tevin Coleman, who was signed as a free agent in the offseason. The latest injury could hurt his chances to impress the coaches and stay at the top of the depth chart.
San Francisco will be happy with its depth in the backfield after problems in the area last season, but the squad will certainly hope Breida can return to the field as soon as possible.