Since npm dropped support for self signed certs yesterday, I can no longer install any packages from npm running on Windows Azure.
On my local machine I could solve
Until we update NPM on Azure, one simple way to work around this is to create a custom deployment script (info here).
Here is a sample repo that demonstrates what to customize: https://github.com/davidebbo-test/AzureNpmCertWorkaround. Specifically, look at this commit, which uses the npm config set ca "" workaround.
If you don't want to deal with generating a custom deployment script using the Azure tool, you can simply grab the .deployment and the deploy.cmd from the test repo, and commit them to the root of your repo.