I haven't tried DoxyWiki.
You could code a wiki Special page like Special:FileSystem or set up a namespace whose "subpages" correspond to doxygen HTML files in the file system. The problem is doxygen wants to render its own navigation which is kinda incompatible with a typical MediaWiki skin's sidebar and such.
You could put the doxygen HTML files in another directory on your web server and link to them. To make this cleaner you could define an interwiki prefix for it, like "docs", and then you can link to the doxygen web pages withh regular wiki links [[docs:php/Action_8php.html|see the Action.php reference docs]]
. You could skin the doxygen output to make it look more like your wiki's skin. But your wiki's search box won't return doxygen matches.