Use a hash for your identifiers. What you did is not perl :(

Here's minimal changes to make it (sort of) work.

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1222918

use strict;
use warnings;
use Tk;

my @meals;
my %identifiers;

my $mf = MainWindow->new;

for (my $j = 1; $j < 7; $j++) {
        my $frame = $mf->Frame(-background => 'alice blue', -padx => 2
+0, -pady => 5)
                ->pack(-expand => 1, -fill => 'both', -side => 'top');
            $frame->Label(-text => $meals[$j-1], 
                        -background => 'alice blue', 
                        -width => 9)
                ->pack(-side => 'left');
            $frame->Text(-height => 6, 
                        -background => 'white', 
                        -width => 25)
                ->pack(-side => 'left');
                
            my $c = 0;
            for (my $i = 2; $i < 9; $i++) {
                if ($c <= 6) {++$c;}
                else {$c = 1;}
                    my $id = $j . $c; # Create identifier
                    $identifiers{$id} = $frame->Text(-height => 6,
                                -background => 'white', 
                                -width => 10)
                        ->pack(-side => 'left');
                } #end for $i
        } # End for $j

$identifiers{'22'}->insert('end', 'R2, C4');

MainLoop;
[download]

I was updating my answer after I realised what "f22" was when tybalt89 wrote this. Which is exactly what my updated suggestion is. Glad we arrived at the same spot though I took the scenic route :)

Separating $i and $j with, say, a dash will save you a bug if and when the number of your widgets increase to 100+: 'f111' can be 1/11 or 11/1

All that message says is that $f22 = undef. Sometimes subs return undef in the case of errors. Because I can not see $f22 anywhere in the code you provided and my knowlegde of Tk is minimal I will stop my answer here. Hopefully it will get you a bit further until others appear.

Update: sorry I spotted my $id = "\$f" . $j . $c; # Create identifier

But you are overriding your identifier in the next line by $id = $frame->Text

Should you perhaps declare a hash before the loops and then save each return of $frame->Text() to that keyed on (ad-hoc) id names? For example:

my %widgets = ();

... # your loops

my $id = "f" . $j . $c; # Create identifier
my $awidget = $frame->Text(-height => 6,
                                -background => 'white', 
                                -width => 10)
                        ->pack(-side => 'left');
die "widget failed $id" if ! defined($awidget);
$widgets{$id} = $awidget;

... # closing the loops
[download]

Then you can access f22 like $widgets->{'f22'}->insert()...

Update #2: $widgets{'f22'}->insert()... is the correct way to access 'f22' widget

Thanks guys. The suggestions work great.