Pittman, the team's top receiver, has been recovering from a quad injury. He caught nine passes for 121 yards and a touchdown in the Week 1 tie against the Houston Texans.
Coach Frank Reich had expressed optimism that Pittman would be able to play after he began experiencing pain Wednesday and was removed from practice.
With the injuries on offense, receivers Parris Campbell and Ashton Dulin and running back/slot receiver Nyheim Hines could see increased roles against the Jaguars. There also could be a bigger workload for star running back Jonathan Taylor, who had 31 carries last week.
McLaughlin, who was signed to the practice squad Tuesday along with Lucas Havrisik, will handle kicking duties against the Jaguars on Sunday.
McLaughlin, who is making his second stint with the Colts after kicking for Indianapolis for part of the 2019 season, will replace Rodrigo Blankenship, who was waived after missing a game-winning attempt against Houston.
McLaughlin said he's spent time on 10 different teams in his four years, making 75.5% of his attempts.
ESPN's Stephen Holder contributed to this report.