You've actually got several options here. The key is that Microsoft Test Manager has to integrate with Team Foundation Server: if you can connect your Selenium tests to Team Foundation Server you can use the Associated Automation field in the test case to link your Selenium test code to MTM test cases.
- Team Foundation Server plugin for Eclipse: this is an official plugin supported by Microsoft that should let you link the test cases within Eclipse. I can't give you any more guidance than that, since I work entirely within the MS development tools, but you can find a decent starting point on the MSDN library: http://msdn.microsoft.com/en-us/library/hh301122.aspx The way it should work is that you should be able to open the test case within Eclipse and set Associated Automation there. Once you've done that there should be a way to wrap the MSTest command line tool to run from Eclipse.
- Link/Compile/Run from Visual Studio: I can't speak to how effective this is, and it may not be an option for you depending on the licensing used where you work, but this article (http://improve.dk/compiling-java-in-visual-studio/) suggests it's possible. The basic method is the same - once the linking is done, running the tests within Visual Studio should simply post to TFS/MTM (or running them using MSTest - which comes with VS and is the command-line tool for test running and the engine that does the heavy lifting).
- Use the TFS API to post your results: This method is a lot more difficult and complex to implement (I've done it, but with C#/Visual Studio), but it can be done. If you can't get any of the other options to work, this is the fallback.
- Run the test cases through MTM: This method is (in theory) possible once you've linked the automation to the test cases, but only if you have the full test lab/test environment configuration and correctly configured test virtual machines to run it on. I honestly don't know if this is possible for you, but it can be done. I'd presume you'd need to have the VS configuration for running Java on each system.
I'd suggest that if possible you try for connecting and running from VS first, simply because if you can work through the VS testing environment and you have the test cases linked to your automation the integration is completely seamless - you run the tests, and then when you open MTM the test results are there.
If you find you need more information on working with the TFS API, I can point you to some good resources on that topic.