If you get this error when you start the server, it probably means that your version of Perl was itself compiled with a shared library called libperl.so. mod_perl detects this and links the Apache executable to the same Perl shared library. This error simply means that the shared library cannot be found by searching the paths that Apache knows about.
Make sure you have Perl installed on the machine, and that you have libperl.so in <perlroot>/<version>/<architecture>/CORE (for example, /usr/local/lib/perl5/5.6.1/sun4-solaris/CORE).
If the file is there but you still get the error, you should include the directory in which the file is located in the environment variable LD_LIBRARY_PATH (or the equivalent variable for your operating system). Under normal circumstances, Apache should have had the library path configured properly at compile time; if Apache was misconfigured, adding the path to LD_LIBRARY_PATH manually will help Apache find the shared library.