It likely won't hit them until their season opener against the Denver Broncos on Sept. 7.
But Colts coach Chuck Pagano is confident that his team "will get through" whatever challenges they face without Mathis.
The Colts will face adversity and less-than-ideal circumstances as they try to make up for the loss of Mathis, the backbone of their defense who recorded 19.5 sacks last season.
"We'll get through this, we'll come together as a team, we'll come together as a family, we'll come together as an organization and we'll get through this," Pagano said Saturday afternoon. "We love and respect Robert Mathis. He's a horseshoe guy, he's a pillar guy.
"Like I said before, we've got his back. Everybody in this organization has his back, and we'll get through this and at the end of the day, we'll all be better for it."
Mathis was suspended Friday for violating the league's ban on performance-enhancing substances. The linebacker said in a statement he was seeking fertility assistance, acknowledging that he and his wife are expecting a baby.
Mathis is not eligible to return to the Colts' active roster until Sept. 29, the day after their game against the Tennessee Titans.
Pagano said it's way too early to name a replacement for Mathis at outside linebacker, but second-year player Bjoern Werner will likely get the first chance to step into the starting lineup.
Werner, the Colts' first-round draft pick in 2013, had 18 tackles and 2.5 sacks as a rookie.
"Somebody will take advantage of the opportunity and play great football," Pagano said. "We've got each others' back and we'll find a way to get through it."