I am also having the same issue. I was able to open it by right clicking on the icon and choosing the 'open' option. However this just made things worse... It says that the new launcher isn't supported on mac 10.5.8. So we can't play the new version of Minecraft 1.6.
And now I am stuck, because the new launcher replaced my old one and I cannot find anywhere on the Minecraft website to download the old launcher. So now I can't even play at all...
Yep. I get the same pop-up. Hope they fix this soon! I was really looking forward to the update.