Byrd, who has multiple facial fractures, was back on the field with his teammate before Wednesday's game against the Houston Astros, playing catch and running for the first time since he took a fastball under his left eye from Boston's Alfredo Aceves.
"I'm not really sure [when I will be back]," Byrd said. "They are looking at four to six weeks, and I think that timetable is about right. You can't rush the fractures. That takes time to heal."
If Byrd and the doctors are correct in their assessment, Byrd could be back for the White Sox-Cubs series July 1-3 at Wrigley Field.
Byrd, who told ESPN Chicago that he will travel with the team to St. Louis on Friday for the weekend series against the Cardinals, said his only real fear was losing his eyesight initially after getting beaned.
"I didn't want to lose my vision," Byrd said. "The re-bleeding, they were worried about that. The clot, making sure that healed and washed away. And the pressure in the eye, they didn't want to mess with that. I got off the dilating drops. I'm still on the steroid drops. I've got an appointment [Wednesday], and hopefully I can get a full clean bill of health."
Byrd said he still has not heard from Aceves even though people told him the Red Sox pitcher tried to contact him.
Byrd, who is batting .308 with three home runs and 11 RBIs in 44 games this season, is looking forward to stepping into the batter's box soon.
"I know I will be fine," Byrd said. "At the same time, you're not sure really how you are going to react. But I'm so excited to be back in there and start swinging again because I love this. We'll see once that first ball comes at you, we'll see what happens.
Bruce Levine covers the Cubs for ESPNChicago.com and ESPN 1000.