First you need to determine if this is, in fact, bamboo growing up into your house.  We can't say for sure from the photo.  We'd recommend that you pull out as much as possible.  Do you see roots?  You can then send us another photo of what you pull out so we can identify it positively. 

(The leaves look somewhat like those of Tree of Heaven.  Crush a leaf.  If it smells like rotten peanut butter, it could be that.  But how did a seed get there?)

Assuming it is bamboo, we can give you instructions for killing it and all the bamboo in your yard.  There are brief instructions for controlling bamboo on our website publication, "Bamboo" on page 2: http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG28%20Bamboo.pdf

How close is your neighbor's property line? This is the first time we've seen bamboo invade a house.  We'd recommend that you contact your county councilman and state delegate letting them know about the situation and requesting some kind of legislation that makes people responsible for the spread of their bamboo.  Eradicating it can be very expensive.
ECN

Thanks! I will follow your recommendations and keep you posted. I've asked the University Park Handyman to assist me since this sprout is very high and near the ceiling. Last year, or perhaps it was the year before, (I will check and I believe I have photos) there was a similar sprout coming up from a lower level at the ktchen countertop/wall (same wall as this sprout.)  It pushed a little piece of side counter away from the wall, and friends and I speculated it was a bread seed that dropped in. I removed that sprout along with a very long root the other year, and it didn't seem to return, but perhaps this higher sprout could be from the same system?!?!

My neighbor's property line is very close to the kitchen where this vegetation has appeared. I will measure the distance and get back with you, but meanwhile I have attached three photos that I have handy of my house and the neighboring bamboo. The neighbors' wooden fence was collapsing in my yard (along with their bamboo which when topped with snow laid flat along the entire width of my yard which I tripped on until I could cut it away!) so I had a chain link fence installed to keep some definition of the two yards, keep their fence and bamboo from falling on me and my dog. My neighbors are very nice; I love them dearly; sadly, they seem to have a sentimental attachment to the bamboo which their deceased husband and father planted decades ago for shade. I'm not sure why they have let it take over their backyard, except for sentiment perhaps. I strive to always get along with my neighbors, and will let them know about this once we've determined if the home invasion is from bamboo or Tree of Heaven (the neighbors may have Tree of Heaven, too) but I can't imagine asking them to take any action or pay for anything. Sigh . . .

Please do send us that photo of the shoot in your kitchen after you remove it so we can get a better look at the leaves and stem, and possibly the root.

Your neighbors may not want remove all the bamboo, but they may be willing to follow the steps in the Bamboo publication in order to at least control their bamboo. 

It would not be costly to spray with an herbicide.
ECN