Iglesias, acquired from the Boston Red Sox in July in a three-team trade, is considered a potential Gold Glove infielder. He said he had pain in both shins last season.
"I was able to play through it last year, but that's not going to happen this year," he told reporters. "That's why it doesn't get better."
The Tigers announced Sunday that Iglesias would begin the season on the disabled list. He is scheduled to visit a foot and ankle specialist, Thomas Clanton of the Steadman Clinic, on Tuesday.
"I'll get a better idea when I see the doctor in Colorado," Iglesias said, according to MLB.com. "But for now, my goal is to get healthy, get rid of this, because the pain is really bad. I just want to get rid of it and come back 100 percent."
Iglesias said he was told of the stress fractures diagnosis in the past few days.
"I've been doing every kind of treatment, but the pain is still really high," he said, according to mlive.com. "It makes sense now because it's a fracture. It's not going to go down until the fracture is better."
Tigers manager Brad Ausmus said Monday he is not going to worry about how much time Iglesias might miss as a result of the injuries.
"You learn, as a player, you can't control it. You take the 25 players that are starting the season and try to find a way to win on a daily basis," he said, according to the Detroit Free Press. "You don't bury your face in your hands, crying about what could have been. It's counterproductive."
The Tigers have no clear replacement for Iglesias on the roster. Utilitymen Steve Lombardozzi and Danny Worth and minor leaguers Hernan Perez and Eugenio Suarez have been playing shortstop in the Grapefruit League while Iglesias has been out of the lineup.
If the Tigers decide to look outside the organization for a replacement, one possibility is free agent Stephen Drew, who hit .253 with 13 homers and 67 RBIs in 124 games with Boston last season. Drew remains unsigned four months after declining a $14.1 million qualifying offer from the Red Sox.
Drew and Iglesias both played for the Red Sox last season before the latter was dealt to the Tigers just before the trade deadline.
If the Tigers decide to explore the trade market for a cheaper alternative to Drew, Seattle's Nick Franklin is another possibility. He was displaced as Seattle's second baseman when the Mariners signed Robinson Cano to a 10-year, $240 million contract over the winter.
ESPN.com's Jerry Crasnick contributed to this report.