Yes many of the answers here are pointing to the correct path, but my case:- I was given a url to access git repos on azure cloud for which I'm perfectly fine to access/browse the code on browser (Vs) when I'm trying to clone I've got the same issue.
So when you click on clone as shown in below image, you've got to Generate Git credentials; this is weird, not sure why, probably they've setup my account to access azure cloud, which can't be used to clone git repos(means can't be used as git credentials). This is something different from what I've seen with AWS/gitlab/bitbucket, maybe an issue with account setup, or if it's common thing for repos on Azure and if you're in same issue - give it a try. 
Another one, as everyone has already mentioned, please don't try to connect to url which is produced over there (something looks like):
https://project-account@dev.azure.com/project-name/apps/_git/library/
Instead try to connect thru your GIT username and then use password:
https://username@dev.azure.com/project-name/apps/_git/library/
As a tip: if your username has special characters in it, Git cmd/bash will throw errors, so replace those with valid characters, ex. :-
- @ can be replaced with %40
- + can be replaced with %2B
something like : https://username%40xyz.com@dev.azure.com/project-name/apps/_git/library/