It seems highly unlikely, except for the previously mentioned gas giants which are mostly hydrogen. Perhaps a planet can form an iron core like the Earth and then have its outer core sheared off by some catastrophe? Or melted off?
The heavier elements typically find their way into stellar nurseries due to supernovae, and this means a pretty good mix of heavier elements are all intermixed, having been formed in layers in the star prior to the explosion, and formed from the explosion itself. It would probably be difficult for these to just separate into individual elements naturally. I'm sure there may be cases with higher concentrations of iron or silicon due to a succession of similar stars creating similar elements, but I doubt you'd ever see 100%.
I think the closest thing you have in the universe is a neutron star, which is just one big pile of neutrons.