The official way to disable the popup is this:

1. Pack your extension: go to chrome://extensions, check Developer mode and click Pack extension
2. Install the extension by dragging and dropping the .crx file into the chrome://extensions page.

You’ll get an “Unsupported extensions disabled” popup if you try restarting Chrome at this point.

Then for Windows 7 or Windows 8:

3. Download Chrome group policy templates here
4. Copy [zip]\windows\admx\chrome.admx to c:\windows\policydefinitions
5. Copy [zip]\windows\admx\[yourlanguage]\chrome.adml to c:\windows\policydefinitions\[yourlanguage]\chrome.adml (not c:\windows\[yourlanguage])
6. In Chrome, go to the Extensions page: chrome://extensions
7. Check Developer Mode
8. Scroll down the list of disabled extensions and note the ID(s) of the extensions you want to enable.
9. Click Start > Run, type gpedit.msc and hit enter.
10. Click User Configuration > Administrative Templates > Google Chrome > Extensions
11. Double click Configure extension installation whitelist policy
12. Select Enabled, and click Show
13. In the list, enter the ID(s) of the extensions you noted in Step 7
14. Click OK and restart Chrome.

That’s it!

EDIT: As of July 2018, this approach no longer works: it seems Google has stopped honouring the “whitelist”.

EDIT 2: As of December 2018, this approach works in Chrome Version 69.0.3497.100 (Official Build) (64-bit):

1. Temporarily enable Developer mode in chrome://extensions
2. Uninstall the extension that causes the popup using the Load unpacked.
3. Click on Pack extension, and find and select the folder containing the extension files. Don’t enter the private key file if you don’t have it.
4. Click Pack extension. A .crx and .pem file will be created near the root directory of the extension. Install the extension using the .crx file and keep the .pem file safe.
5. Copy the .crx installed extension ID to the whitelist and restart Chrome.

The popup should be gone.