>perl -wMstrict -le
"my $c   = 'A';
 my $min = 3;
 ;;
 my $s = 'uuAvvAAwwAAAxxAAAAyy';
 ;;
 printf qq{'$1' } while $s =~ m{ ([[:lower:]] (?:$c){$min,} [[:lower:]
+]) }xmsg;
"
'wAAAx' 'xAAAAy'
[download]

Update: The quantified sub-pattern in  (?:$c){$min,} needs to be enclosed in a group (non-capturing or capturing) because otherwise  $c{$min,} looks to Perl too much like the interpolation of a scalar hash element from the  %c hash.

Further Update: Interesting. I was unaware of the  \ (backslash) disambiguation pointed out below.

Further Further Update: Or maybe not so interesting, since the regex doesn't actually seem to match anything:

>perl -wMstrict -le
"my $c   = 'A';
 my $min = 3;
 $_ = 'AAAAAA';
 print 'match' if /($c\{$min,})/;
 print qq{'$1'};
"
Use of uninitialized value $1 in concatenation (.) or string at -e lin
+e 1.
''
[download]

Yet Another Update: It is also possible to use a constant, but it's kinda messy. A Readonly scalar might do a better job for you.

>perl -wMstrict -le
"use constant MIN => 3;
 my $c = 'A';
 ;;
 my $s = 'uuAvvAAwwAAAxxAAAAyy';
 ;;
 printf qq{'$1' }
   while $s =~ m{ ([[:lower:]] (?:$c){${ \MIN },} [[:lower:]]) }xmsg;
"
'wAAAx' 'xAAAAy'
[download]