Rodriguez is slated to start and play at least three innings at third base for Class A Charleston, S.C., on Tuesday night.
Rodriguez has been working out at the Yankees' spring training complex in Florida this year while recovering from surgery on his left hip on Jan. 16. The three-time AL MVP turns 38 later this month.
"That is definitely a step in the right direction," said Yankees manager Joe Girardi. "He has the 20 days starting tomorrow, and he must feel pretty good. He must be moving pretty well. We'll see how it goes.
"I expect him to be a productive player. The last time he got his hip fixed he came back productive, and hopefully this will solve some of the things that he was dealing with last year. I expect him to be productive. I can't tell you exactly what he's going to do, but I think he's going to be a good player."
Derek Jeter also moved a step closer to rehab assignment when he ran the bases at the team's complex in Tampa, according to Newsday.
Rodriguez on Monday said he felt fine and was eager to get going.
"Awesome," he said at the Yankees' spring training complex in Tampa, Fla. "I'm really excited."
He later added via spokesman: "Had another good workout today and feel great, and I'm excited to get back on the field tomorrow."
Rodriguez has yet to play this season after undergoing hip surgery in mid-January. MLB officials are also investigating his alleged role in the Biogenesis scandal.
His rehabilitation became a point of contention last week.
Rodriguez tweeted last Tuesday that he had been cleared to play rehab games by his surgeon, Dr. Bryan Kelly, which prompted general manager Brian Cashman to tell ESPNNewYork.com's Andrew Marchand that A-Rod should "shut the f--- up."
When asked whether everything is OK with the Yankees, Rodriguez on Saturday said, "Absolutely."
"Ready to get back on the field," he said. "All good."
Rodriguez hit .272 with 18 home runs and 57 RBIs last season. His replacements have struggled. Kevin Youkilis is out for the foreseeable future after having surgery to repair a herniated disk in his back, while David Adams is hitting just .186 in 102 at-bats.
"We need Alex back," Yankees president Randy Levine told ESPNNewYork.com's Ian O'Connor by phone this past weekend.
"How effective he'll be when he comes back, how good he'll be, we don't know. But we are desperate for his right-handed power, and he's better than any third baseman on this team right now."
"We've had trouble scoring runs, but that's no secret," said Girardi. "It'd be nice to get some big bats back."
Information from ESPNNewYork.com's Mike Mazzeo, Andrew Marchand, Ian O'Connor, Wallace Matthews and The Associated Press was used in this report.