Lindsay, a rookie who rushed for 1,037 yards this season, suffered ligament damage and a possible fracture to one of the small bones of the wrist in Monday's loss to the Oakland Raiders.
Tests on Christmas Day revealed the ligament damage, and Lindsay was slated to get a second opinion to see if there was also a fracture.
"I'm not sure what they found, but it needs surgery," Joseph said after Wednesday's practice. "It's going to be about a three-, four-month rehab. He'll be fine.''
Joseph said the Broncos will consider formally moving Lindsay to injured reserve in the coming days. He will miss the Pro Bowl after being named to the AFC roster earlier this month.
Lindsay finished just shy of Dominic Rhodes' NFL record of 1,104 rushing yards by an undrafted rookie. Lindsay also had nine rushing touchdowns and is tied for second in the league with an average of 5.4 yards per carry.
Fellow rookie Royce Freeman likely will get the start in Sunday's regular-season finale against the Los Angeles Chargers, while Devontae Booker should see action in longer-yardage situations, especially third down.