Did you do a clean install, or migrate?
What version of InDesign are you trying to run?
I have two computers (MacBook Pro and iMac) which have been running InDesign CS6 and CC just fine in Mavericks since it came out.
If you migrated from another computer, that does not work. You'll have to use the Adobe Cleaner tool and install fresh from Creative Cloud or from a backup download or disc.