What you're seeing is also found with the 5D Mark II, 5D Mark III, 1DX, 7D ... I suspect almost every Canon DSLR with the only possible exceptions being those cameras that have been released in the last 12 months (1DX Mark II, 5Ds/R and maybe 80D.)
There's nothing to do except try to clean it up in post as best you can. Right now, the only way to solve this problem for sure is to use a non-Canon DSLR - i.e. get a Sony A7II/A7RII and use an adapter to fit a lens.