I have a bone in my arm.

The speaker offers a playful excuse for not doing something with their arm, such as reaching for an object. Having a bone in the arm is presented as though it prevented the action.

The excuse is deliberately absurd: an ordinary part of the body cannot explain the refusal. The saying conveys unwillingness to help without suggesting that the speaker is injured.

Use it as a humorous response when someone asks you to do something or reach for an object on their behalf. It works as a light refusal because the listener can recognize that the supposed obstacle is no obstacle at all.