Simply edit your .conkyrc file and add the following line:
${font DejaVu Sans Mono :size=8}${exec cal -m | cut -c23-44 --complement}
Some explanation:
The Font - Yep, you have to use that font, otherwise it wont come out right.
"cal -m" - If you want Sunday to be the first day of the week simply remove the -m.
If you are having any problems, please post in the comment field (no registration required and I will try to help you out).
Thanks!
UPDATE (Debian Users):
Unfortunately "cal" doesn't support weeks starting with monday anymore. The fix:
apt-get install gcal
New line for conkyrc;
${font DejaVu Sans Mono :size=8}${exec gcal --starting-day=monday | cut -c23-44 --complement}