I have two scripts, namely shell_script.sh and perl_script.pl. 
shell_script.sh : It has function definitions which, when invoked from Perl script, will execute certain commands on Linux in batch mode.
perl_script.pl : It has the code and logic to be implemented, which functions to invoke etc.
The content of shell_script.sh file is as under:
bash-4.2$ cat shell_script.sh
#!/bin/bash
# Function Definitions
func_1 ()
{
  echo "function definition"
}
func_2 ()
{
  echo "function definition"
}
The content of perl_script.pl file is as under:
bash-4.2$ cat perl_script.pl
#!/usr/bin/perl
use Getopt::Long;
my $var1;
my $var1;
GetOptions("var1=s"     => \$var1,
       "var2=s" => \$var2,
       "help|?" => \$help );
if ($help)
{
    HelpMenu();
}
print " Can I call the func_1 (defined in shell script) with arguments here..?? (in this perl script)";
How can i invoke the function func_1() (which is defined in shell_script.sh) in the perl script perl_script.pl ?
To invoke a shell function, the shell needs to know its definition. One way to achieve that is to have the shell first source the file which defines the function. And then, without exiting the shell, call the function. From a Perl script, that would be for example:
system 'bash', '-c', 'source shell_script.sh; func_1';
                        To use bash functions you need to be in bash. So that puts you inside backticks or system when in a Perl script, where you are inside a bash process†.  Then, inside that process, you can source the script with functions, what will bring them in, and execute them
funcs.sh
#!/bin/bash
function f1 {
    t1=$1
    u1=$2
    echo "f1: t1=$t1 u1=$u1"
}
function f2 {
    t2=$1
    u2=$2
    echo "f2: t2=$t2 u2=$u2"
}
and in Perl (one-liner)
perl -wE'
    @r = qx(source funcs.sh; f1 a1 b1; f2 a2 b2); 
    print "got: $_" for @r
'
where qx is the operator for backticks, but perhaps clearer.  I use backticks in case  you need return from those functions. If your /bin/sh isn't linked to bash† then call bash explicitly
perl -wE'
    @r = qx(/bin/bash -c "source funcs.sh; f1 a1 b1; f2 a2 b2"); 
    print "got: $_" for @r
'
Assignment to an array puts qx in list context, in which it returns the STDOUT of what it ran as a list of lines. This can be used to separate return from different functions, if they return a single line each.  The a1,b1 and a2,b2 are arguments passed to f1 and f2.
Prints
got: f1: t1=a1 u1=b1 got: f2: t2=a2 u2=b2
This makes some (reasonable) assumptions.
If there is no need for the return, but the functions only need to do their thing, you can use
system('/bin/bash', '-c', 'source ... ') 
as in Håkon's answer
†  It is /bin/sh really, but that is often relegated to bash. Check your system (/bin/sh is likely a link to another shell). Or ensure that bash runs the command
my @ret = qx( /bin/bash -c "source base.sh; f1 a1 b1; f2 a2 b2" );
See text for the explanation of this example.
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