This was a significant step for Martinez, who began catching bullpen sessions last week.
When the Indians head off to Minnesota to begin a three-city, nine-game road trip on Friday, Martinez, who is still slated to return to the Tribe sometime in mid-August, will be with them.
"I want him around a lot more," manager Eric Wedge said. "He's one of the leaders on this ballclub. It's tough for the guys on the DL. They can't be around all the time, because they'll go crazy. But now that he can see the light at the end of the tunnel, it will be good to have him around."
One guy who is not around is Hafner, who had to head back home to North Dakota over the weekend because of an undisclosed family emergency.
Hafner, who has been on the DL since May 30 and was transferred to the 60-day DL on Saturday, was supposed to have the latest strength test performed on his right shoulder Monday, but that plan was temporarily scrapped. Hafner's last test revealed that his right shoulder had 65 percent of the strength of his left shoulder.
"We're not sure when he's going to be back," Wedge said.
Infielder Jamey Carroll was out of action on Monday night. He did some agility drills before batting practice to test the left hamstring he strained Friday, but he was still not ready to be in the lineup. Wedge wasn't sure if Carroll would be available off the bench.
Anthony Castrovince is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.