Moving out of AE SDK subforum to main AE forum
MKV is only a container it is not a codek. Are several articles available on the Google search that will tell you how to convert them to a format that AE and Premiere Pro can use. The format is not currently supported: Importing and interpreting footage items in After Effects
Some MKV files may work because of the codec used for compression but you're kind of on your own here. I would convert them to a good production quality format.
MKV files need to be unpacked/ converted using Handbrake or similar tools. As Rick said it would be smart to read up on that stuff. You don't even seem to have an idea what an MKV file actually is in technical terms.
First question: What video and audio formats are contained in your Matroska (MKV) file?
If it's H.264/mpeg4 video, it's a very simple task to use XMedia Recode (Windows only - so please state if you're a Mac or Linux user, in that case you should use either Hybrid or Handbrake CLI) to switch to the MP4 container format.
If even the video format isn't recognized by Premiere such as Google's new VP9 video format, you are forced to transcode the video into another format. That means you risk losing quality + it will take you a lot more time to get started. You can use any of the tools linked above to do the conversion as well.
(Note: Just like Apple, Adobe also doesn't really like (technically superior) open source multimedia formats - something that is a pain in the arse for far more of their users than both companies would like to admit).
Always keep your original MKV files. It is by far the best storage format for video content. You can see why here: