Many fonts on Typekit support German. You can filter for fonts that support German by selecting "German" from the Language Support section on http://typekit.com/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: