You can see in Inkscape (and in GIMP, too) as one of the coloring options CMYK. It will show for ex. pure max. bright green RGB(0,255,0) as CMYK(100%, 0%, 100%, 0%) which is plausible.
It's also exact if you have a CMYK color producing mechanism which creates all sRGB colors with the simplest possible linear transformation.
But Inkscape cannot output CMYK color files, CMYK exists only as a color selection possibility. Even worse problem with Inkscape and CMYK is that Inkscape knows nothing of real CMYK printing.
One can find easily in document settings and program preferences some interesting dialogs, but they do nothing, they are still only beautiful dreams. An example:
The shown text Euroscale Coated v2 is the name of one generic CMYK printing color profile.
The transformation between normal on the screen RGB colors and printed CMYK colors is extremely complex, non-linear and depends strongly on the used print process and paper. Generally only a part of onscreen RGB colors are possible in usual CMYK printing processes.
That's one good reason why Adobe succeeds to collect high profits year after year. Adobe's programs know the conversion between real CMYK printable colors and the usual RGB. People select the right CMYK printing color profile into use and see on the screen what they will get from the printer. Programs also flag possible unprintable colors and help user's to avoid the printed muddy mess which would come out if one makes his design with bright RGB colors and transforms them to CMYK like Inkscape does, not by having the right CMYK print process color profile.
As said already in the other answer, Scribus understands CMYK print process color profiles and can help you to see the realistic result if you import your file to Scribus and convert it to CMYK.
Unfortunately it isn't available in the fly as you create a new design in Inkscape like a realistic result can be seen in Adobe's programs during the design. Edit: Not true! See the fixes at the end of the answer.
Krita is another freebie which knows realistic CMYK printing and can show the result during the design work. Serif Affinity series do the same with low cost.
Another useful idea would be to decide the color palette in a CMYK printing conscious program. The RGB conversions of those colors could be used in Inkscape and see the realistic result in the fly.
ADD in May 2022: GIMP 2.10 understands CMYK print profiles, it can show the CMYK printing result and can warn if something is unprintable in CMYK. This all is availabe in the real time when one edits his RGB image in GIMP. The actual conversion to CMYK must still be done outside GIMP, for ex. in Krita, if one wants to use Freeware.
Add in September 2022 If one has both Inkscape and Scribus properly installed, the Inkscape dialogs shown above start to work so that the CMYK printing result of the RGB drawing can be directly previewed. That's been said in another answer one and half an year ago. It doesn't work if the programs are executed as separated by some sandboxing system which prevents them to see each other.
Yes, kind of - there's built-in Color management, built-in print preview and CMYK PDF export included with Inkscape. It requires Scribus to be installed, though, for this to work, and your file to be set up correctly.
More details are available at https://wiki.inkscape.org/wiki/index.php/Release_notes/1.0.1#Color-managed_PDF_export_using_Scribus
The simplest way to convert pdf from inscape to CMYK is by using ghostscript. I did a batch file on Windows and just drag&drop pdf file on it in Explorer. The result isn't the best possible, but ghostscript allows us to use CMYK color profiles, so we can mess up with this and find the suitable result.