Don't think so. The R9 290 that I had did not have HDMI 2.0. Doubt that the 290x would since they're fairly similar cards.
Your best bet would be to wait a bit for AMD's 300 series cards; they should be released at the end of Q2 2015.
Belkin is selling a Mini-DP to HDMI 2 for 4K output via the Apple Store, but the product description is confusing and reports are conflicting as to weather it works. Curious on this one as Apple is usually quite demanding if they are reselling something (on top of the Apple tax).
BTW, HDMI is just a repackaging of DP with extra royalties being paid out so not a big difference.
Link : http://store.apple.com/us/product/HGFB2ZM/A/belkin-4k-mini-displayport-to-hdmi-adapter?fnode=51