"I'm excited for training camp; however, I'm disappointed I won't be there with the team as we start," Reich said in a news release.
"I'm fortunate to be fully vaccinated and I'm asymptomatic. I'm feeling well and I'm looking forward to returning as soon as I'm medically cleared."
Colts rookies reported to camp Saturday. Veterans are scheduled to report Tuesday to Grand Park Sports Campus. The Colts' first practice is scheduled for Wednesday morning in Westfield.
Colts general manager Chris Ballard told reporters Monday that Aug. 2 is the earliest day Reich can return to camp. Reich received his positive test result late last week. Ballard also said that a staff member tested positive for COVID-19.
Reich still plans to use Zoom video conferences to stay in contact with players and staff.
NFL COVID-19 protocol allows for fully vaccinated and asymptomatic people to return to work after two negative test results that surface at least 24 hours apart.
"We are going to be careful," Ballard told reporters. "We are going to be safe. When he is back, he is back."
Ballard said more than 60% of Colts players have received at least one shot of a COVID-19 vaccine.
The Colts will face the Carolina Panthers in their first preseason game at 1 p.m. EDT Aug. 15 at Lucas Oil Stadium in Indianapolis. They will start the regular season against the Seattle Seahawks on Sept. 12 in Indianapolis.