First we need to understand if you're actually shooting at "macro" focusing distances, or just "close-up."
Life-size is the typical aim of "full macro" shots, which is to say you are working at a 1:1 reproduction ratio, shooting very small objects at close range. Insects, flower stamens, etc. There are two problems typically encountered here that are tightly related: thin depth of field, and camera movement. You're working in such a small area that the slightest movement completely changes your composition, and depth of field is so slim that even with the smallest apertures you're fighting to get everything in focus. You're also fighting to get the camera's shadow out of the frame, and traditional camera-mounted flash is useless because it shoots above your subject since the camera is so close. Because you're fighting DOF you are often shooting smaller apertures and creating longer exposures, too. A tripod is basically a necessity if you're working on still subjects, and a focusing rail may also be useful/required. For moving subjects... well, just find a composition you like, and wait for the subject to come to you. Tracking a frame-filling bee, for example, is basically impossible.
Close-ups are what most people mean when they say "macro." Your subject is typically small -- a model train, perhaps -- and you are working at relatively close range. The process for shooting is very much like any other shot, though, where you just need to have good technique to get the photo you want. Your camera-mounted flash may even be enough to reasonably light the subject. You can typically use the support you prefer or require based upon shutter speeds.
Monopods have their place, but realize that their absolute stability is definitely less than a tripod can offer. While a monopod may help you get better shots, I'm sure a tripod would, too, and will let you get shots the monopod would not. If you've been taking photos that are just not quite sharp enough, then a monopod is probably a fine choice; otherwise I would recommend a tripod.