UPDATE 2 Since Git 2.5.0 the feature described below can be enabled on server side with configuration variable uploadpack.allowReachableSHA1InWant, here the GitHub feature request and the GitHub commit enabling this feature. Note that some Git servers activate this option by default, e.g. Bitbucket Server enabled it since version 5.5+. See this answer on Stackexchange for a exmple of how to activate the configuration option.
UPDATE 1 For Git versions 1.7 < v < 2.5 use git clone and git reset, as described in Vaibhav Bajpai’s answer
If you don’t want to fetch the full repository then you probably shouldn’t be using clone. You can always just use fetch to choose the branch that you want to fetch. I’m not an hg expert so I don’t know the details of -r but in git you can do something like this.
# make a new blank repository in the current directory git init # add a remote git remote add origin url://to/source/repository # fetch a commit (or branch or tag) of interest # Note: the full history up to this commit will be retrieved unless # you limit it with '--depth=...' or '--shallow-since=...' git fetch origin <sha1-of-commit-of-interest> # reset this repository's master branch to the commit of interest git reset --hard FETCH_HEAD