Change the theme itself... To be honest there's no real solution to this. Selecting text changes it's background, and the Solarized theme has set this background color to the text color that may sometimes be used.
Although AFAIK there should be no text with this color if I remember right...
I did a bit of digging in the theme file and found the culprit. This color (0x073642), which the original solarized theme defines as strictly a background color (base02), is used for text associated with "storage". It's easy enough to change, but still a hassle since it will be overwritten with updates. I assume this is an issue that goes back to the original Textmate theme, but I'd really like to see it fixed.
I have been using Solarized all since it first appeared, both with TextMate and Sublime Text. It always bothered me that the selection is so dark though, so the first thing I do is to change the selection color to #DDDDDD. OK, this color is not really part of the Solarized palette, but it works great for me and does not clash with anything else.
For Sublime Text 3 you can make the changes to a copy of Color Scheme - Default/Solarized (Light).tmTheme inside your Packages folder. That way it will not be touched if the original file is updated.