Burnett has been cleared to resume workouts as part of a return-to-pitch progression. He rode an exercise bike and played catch for 50 throws in the bullpen.
Burnett said the Pirates will take a conservative approach to his rehab. He is expected to be out two to three months.
"The first few (throws) were a little hairy, I'm not going to lie," Burnett said. "But it went fine. I've got a lot of catching up to do. I'm glad to be back down here with the guys."
The Pirates acquired Burnett on the first day of spring training in a three-player trade with the New York Yankees. He was injured Feb. 29 when he fouled a ball off his right eye during a bunting drill.
Burnett had surgery March 2 at Allegheny General Hospital in Pittsburgh.
"There's not much I could've done, other than pull the bat back," Burnett said. "You can't look back at it. I had my day of tears, lying in the hotel room wondering why it happened. I'm over that now. I want to move in a positive direction and get back on the field."
To repair the fracture, Dr. Randall Beatty attached a thumb-sized piece of plastic onto the bone.
Burnett said choosing to have surgery was a "no-brainer" because he otherwise would have run the risk of developing double vision. Burnett's right eye was swollen shut for a few days after the injury happened and was slightly blurry later, but he said is vision now is fine.
"For what I do, my eyesight is pretty important, so why take a chance of it not healing the right way," Burnett said. "They could've let it heal, but there's a chance it wouldn't heal smooth, the eye wouldn't move right and there'd be double vision."