I'd recommend a scratch test along the brown part to see if there's live tissue beneath - take a fingernail and gently scratch a thin layer off and if there's green underneath then the plant is still trying to send nutrients to that section.
That said, the appearance leads me to suspect that the green you see on the tip of that section is not from the bamboo. If the scratch test confirms that the section is dead, I'd recommend pruning with some clean sharp shears closer to the main stem (but not so close you cut the main stem where they join).