Garrett said Martin's contract situation was the reason for his decision. Martin did show up at the team's training complex and went through a regular workout on his own Tuesday.
Martin, 27, is set to play this season on the fifth-year option of his rookie contract. He will earn a base salary of $9.3 million.
"Obviously, there's a contract situation going on there -- the business of the NFL," Garrett said Wednesday. "We'll see how that gets resolved here. But that's really the reason he hasn't practiced up to this point."
Martin has not missed a game since the Cowboys selected him with the 16th overall pick of the 2014 NFL Draft out of Notre Dame.
The 6-foot-4, 315-pound Martin is expected to attend the Cowboys' mandatory three-day minicamp on June 12-14.
Martin said last week that his focus is squarely on the upcoming season, per 247Sports.
"I think it's been better after we've gotten into the facility with all the guys," Martin said. "I really don't think about it now, because I'm with those guys working out and kind of back to normal. We'll see. Hopefully it gets done. We'll see where it goes."