Many fonts on Typekit support German. You can browse fonts that support German by selecting "German" from the list of supported languages in the sidebar under browse fonts.
German is included in the default option, so the German characters will be available to your website within a few minutes of publishing your kit.
You may also create a custom language subset which includes German, to reduce the size of your kit. The Language Support & Subsetting help page has more information on the character set options.
All fonts that support German include the following letter characters, at minimum: