Is there a way to remove the history for a single file in Mercurial?

It is correct that you cannot easily remove a particular file from Mercurial in the sense that doing so will disrupt all the changeset IDs in your repository. When you change the changeset IDs, everybody has to re-clone the repository. See the Wiki page about editing history for information about the consequences of modifying the history in Mercurial.

If that is okay to you (internal repository in a company), then take a look at the convert extension. It can do hg → hg conversions and has a --filemap argument which can be used to exclude files, among other things.

No, you can't. Read the changes that should have never been section of the mercurial red book about it; and particularly the what about sensitive changes that escape subsection, which contains this paragraph:

Mercurial also does not provide a way to make a file or changeset completely disappear from history, because there is no way to enforce its disappearance; someone could easily modify their copy of Mercurial to ignore such directives. In addition, even if Mercurial provided such a capability, someone who simply hadn't pulled a “make this file disappear” changeset wouldn't be affected by it, nor would web crawlers visiting at the wrong time, disk backups, or other mechanisms. Indeed, no distributed revision control system can make data reliably vanish. Providing the illusion of such control could easily give a false sense of security, and be worse than not providing it at all.

The usual way to revert committed changes is supported by mercurial through the backout command (again, mercurial book: dealing with committed changes) but the information does not disappear from the repository: since you never know who exactly cloned your repository, that would give a false sense of security, as explained above.

It can be done in under 10 min. in a single repository, although there are consequences.

How: use hg convert as described in this excellent guide. Basically, you "convert" an Hg repo into a new Hg repo, but you get to specify a list of files to exclude during conversion. This is an excerpt of the key steps:

Make sure all your teammates have pushed their local changes to the central repo (if any)
Backup your repository
Create a "map.txt" file:

# this filemap is used to exclude specific files
exclude "subdir/filename1.ext"
exclude "subdir/filename2.ext"
exclude "subdir2"

Run this command:
hg convert --filemap map.txt c:/oldrepo c:/newrepo
NOTE: You have to use "forward-slash" in paths, even on windows.
Wait and be patient
Now you have a new repo at c:\newrepo but without the files

As for the consequences...

• all changeset IDs after the files you want to exclude were added will be different
• the new "clean" main repository will have to be manually put in place of the existing one
• all team members will have to make new clones of the main repo
• any other services which integrate with Hg may require attention (e.g. the issue tracker, a code review system etc.)