Actually, in theory, no. Calibration of the two devices is independent. If you calibrate just the printer, perfectly-adjusted images may look wrong on the monitor but will print just fine. You could use images corrected by someone else somewhere (which you download), or you could calibrate "by wire", just looking at histograms and numeric values rather than trusting your eyes, probably in combination with making test prints.

This may sound a bit silly (because, in practice, you really want to calibrate your monitor too), but is actually an important concept to understand in any case, because the range of colors and the degree of contrast which can be displayed on monitors and which can be printed with various inks and various papers differs significantly. Your monitor can show colors which can't be printed, and you can print colors which can't be displayed on screen.

There's a nice 3D diagram of overlap between an Apple LCD and an Epson printer in this article by Keith Cooper, which also covers this whole topic in more depth.

Color management can help you visualize what the results will be, but if it's critical, nothing beats making test prints. If you have a higher-end wide-gamut monitor, you will be able to display almost everything that can be printed with most inks on most paper. Then, the challenge becomes making sure that the colors outside of that space aren't used — or at least, aren't critical. When you go to make your print, these will be "clipped" to in-gamut colors; that is, they'll be automatically reassigned to something the printer software determines to be close enough.

An alternative is to just work in sRGB, which is a constrained color space designed to both display well-enough and print well-enough on most equipment. You lose out on anything that can't be represented by either — and on a little more just to be safe. That sounds bad, but it's actually a big enough space that if absolutely perfect color isn't top on your list of important factors, you might not even notice.