I would say it is possible that it is Phoneutria nigriventer (Brazilian Armed Spider) but even still the red on the back is not something I know in this species. This species is venomous but this is my best guess. More photos would be needed to properly identify the species.
I agree, with the picture is hard to see but as suggested above, I believe it belongs to Phoneutria. The genus is characterized by a prolateral dense 'brush' of hairs (technically called scopula) on the pedipalps (both on the tibiae and tarsi). From what I can tell on the picture, this one may have it. As for the species, even with a well preserved specimen, it is tricky to know and for certainty it is often needed the inspection under the microscope, particularly focusing on the genital structure. Coloration may be useful; however, there is considerable variation and thus is not very reliable. Currently there are eight valid species in the genus with most having a relatively wide distribution. I may be mistaken, but I believe most Phoneutria species may be potentially venomous to humans.
Thanks Jose. although interesting, I don't think it would be necessary (at least from my part). After doing a little bit of research, looking at the known distribution of non-amazonian Phoneutria species (Martins & Brescovit 2007) and given the locality (Davinopolis), it looks that it may be P. nigriventer (as suggested by Matthew) or P. pertyi. More than that I cannot tell...