given a directory where 1 or more perl modules are installed [...], is there a way to determine what version of perl [...] was used to install those modules?

For pure-perl modules, no, because the installation process essentially just copies the module from the source / unpacked archive directory. The installing perl does not leave any "fingerprints".

For XS-based modules, partially. The Perl part is copied as before, so again, no "fingerprints". The C library generated from XS is compiled code, and even when stripped, you should still be able to find some traces in the binary:

>strings /usr/lib64/perl5/vendor_perl/auto/DBI/DBI.so|sort -u|grep -i 
+perl
    Note: perl is running without the recommended perl -w option
PERL_DBI_XSBYPASS
PerlIO_open
PerlIO_printf
PerlIO_puts
PerlIO_vprintf
Perl_PerlIO_close
Perl_PerlIO_flush
... a lot of matches omitted here ...
Perl_sv_upgrade
Perl_taint_proper
Perl_warn_nocontext
Perl_warn_sv
Perl_xs_boot_epilog
Perl_xs_handshake

>
[download]

Well, no version here, but because the XS API changed over time, you should at least be able to elimitate some older versions. E.g. I guess PerlIO functions weren't available in 5.005.

Let's be a little bit smarter and search for a digit followed by a dot:

>strings /usr/lib64/perl5/vendor_perl/auto/DBI/DBI.so|sort -u|grep '[[
+:digit:]]\.'
1.636
GCC: (GNU) 5.3.0
GLIBC_2.2.5
GLIBC_2.3
GLIBC_2.3.4
GLIBC_2.4
bind_col: column %d is not a valid column (1..%d)
v5.22.0

>perl -v

This is perl 5, version 22, subversion 2 (v5.22.2) built for x86_64-li
+nux-thread-multi

Copyright 1987-2015, Larry Wall

Perl may be copied only under the terms of either the Artistic License
+ or the
GNU General Public License, which may be found in the Perl 5 source ki
+t.

Complete documentation for Perl, including FAQ lists, should be found 
+on
this system using "man perl" or "perldoc perl".  If you have access to
+ the
Internet, point your browser at http://www.perl.org/, the Perl Home Pa
+ge.

>perl -MDBI -E 'say $DBI::VERSION'
1.636

>
[download]

That looks about right.

Alexander