The following image appears in Star Wars Blueprints: The Ultimate Collection. Despite being a non-canon source, it appears to be the best representation of a midi-chlorian that we have.
The middle panel is a close-up. The lower picture gives some idea of scale (inside a red blood cell).
George Lucas offered the following description
"Midi-chlorians are a loose depiction of mitochondria, which are
necessary components for cells to divide. They probably had
something--which will come out someday--to do with the beginnings of
life and how one cell decided to become two cells with a little help
from this other little creature who came in, without whom life
couldn't exist. And it's really a way of saying we have hundreds of
little creatures who live on us, and without them, we all would die.
There wouldn't be any life. They are necessary for us; we are
necessary for them. Using them in the metaphor, saying society is the
same way, says we all must get along with each other."
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You can see the similarity between a mitochondrion and a midi-chlorian below.
Electron Microscope picture courtesy of Keith R. Porter