I can't delete a remote master branch on git

As explained in "Deleting your master branch" by Matthew Brett, you need to change your GitHub repo default branch.

You need to go to the GitHub page for your forked repository, and click on the “Settings” button.

Click on the "Branches" tab on the left hand side. There’s a “Default branch” dropdown list near the top of the screen.

From there, select placeholder (where placeholder is the dummy name for your new default branch).

Confirm that you want to change your default branch.

Now you can do (from the command line):

git push origin :master

Or, since 2012, you can delete that same branch directly on GitHub:

That was announced in Sept. 2013, a year after I initially wrote that answer.

For small changes like documentation fixes, typos, or if you’re just a walking software compiler, you can get a lot done in your browser without needing to clone the entire repository to your computer.

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Note: for BitBucket, Tum reports in the comments:

About the same for Bitbucket

Repo -> Settings -> Repository details -> Main branch

To answer the question literally (since GitHub is not in the question title), also be aware of this post over on superuser. EDIT: Answer copied here in relevant part, slightly modified for clarity in square brackets:

You're getting rejected because you're trying to delete the branch that your origin has currently "checked out".

If you have direct access to the repo, you can just open up a shell [in the bare repo] directory and use good old git branch to see what branch origin is currently on. To change it to another branch, you have to use git symbolic-ref HEAD refs/heads/another-branch.

The quickest way is to switch default branch from master to another and you can remove master branch from the web interface.