Surely this is not the one affixed to the wall? You have to be referring to the one with the spindles.
At each end the bannister is attached to something stable like a wall or a post. have you checked the attachments at these points for loose screws or wallered out holes? Do this first.
Are all the spindles attached securely and not wobbling?
If these things are not the cause, then you need to reinforce the bannister and this will be only a bandaid.
On each end of the bannister, you might attach a angle bracket that is small enough not to be readily seen and big enough to assist in reinforcing the bannister. I would suggest an angle support that is about 2 1/2 inches long on each side. Screw this in, do not nail it. Attach this to the underside of the bannister and the other end to the wall. This bracket requires four screws, use each one. The screws need to be long, but not so long that they extend up through the railing part of the bannister. Very important.
Now do the same thing at the other end. you might have to take a hammer and bend or change the angle of these supports, that is OK and necessary. You want to duplicate the same angle as the railing and wall create.
Now paint these supports and see how this helps. Point, these will not work if allot of force is applied to the bannister.
As I said, this is a bandaid and the first line of attack. If this does not work and you have children running around and hanging on the bannister or other things, you need to contact a stair person and have it reattached in an expensive manner.
This is only my opinion on the situation, others may have different ideas.