The famous baker suffered the gruesome injury Sunday while spending some QT with his family in the bowling alley in their home. A rep tells us there was a malfunction with the bowling pinsetter -- a problem the family's had in the past and usually a common fix, but not this time around.

We're told Buddy tried to release a bowling pin from the cage mechanism, but his right hand got lodged and compressed inside the unit. His rep described what happened next this way -- "Unable to remove his hand, [Buddy] can see a 1 1/2" metal rod slowly and repeatedly impale his hand three times between his ring finger and middle finger."

After more than 5 minutes, Buddy still couldn't get his hand free from the metal rod jammed through it. His rep says his sons, Buddy Jr. and Marco, "rushed to the garage for a reciprocating saw to cut through the metal rod" and finally got Buddy's hand free.

Buddy was rushed to a hospital where he underwent emergency surgery to remove the rod and stabilize the wound. A second surgery followed ... performed by renowned orthopedic surgeon Dr. Michelle Carlson in Manhattan.

The rep says Buddy will have an uphill battle given it's his dominant right hand. He faces a long road to recovery and therapy. Buddy's not exactly ready to call this a pinhead move ... but he's definitely kept his sense of humor through this painful ordeal.

He posted a pic Wednesday from his hospital bed with the caption, "I was involved in a terrible accident a few days ago... 😔 What do you think of my new accessory?"

Sending positive vibes, boss!!!