The following is going to go in reverse (from Malaga to Madrid), but you can just flip it. Also, most of the links are in Spanish, but it at least gives you the village names. Lastly, I have not actually walked this, so I can't comment on what the walk is like.
From Malaga to Cordoba, you can follow what forms the first part of the Camino de Santiago desde Malaga (there are camino de santiagos from everywhere, not just the best known one across the north of spain).
http://bit.ly/1xlUcQx (Look for Malaga --> Cordoba, it includes gps tracks and stage descriptions (in spanish), although you have to register with the website to download the gps tracks)
From Cordoba to Toledo, this part is the least documented.
A list of villages through which a path goes is
and this is a plot of the first half of them using google maps and walking
they are not all places you would want to stop (some are just 7km apart) and you would need to find out where you can stay.
From Toledo to Madrid, you can go via Aranjuez or Illescas (again link is just list of villages).
I have done Madrid-Aranjuez by mountain bike and there is quite a nice route, starting from Madrid Rio (easy to get to from anywhere in Madrid) you can follow the bike path south along the river. It then follows a bike path along M-301 for a while, but after that if you take what in link below is the yellow side-detour you are an a dirt track/farm road along a nice rise of hills.
http://bit.ly/1sbMkg2 about 6 years ago