space separation under /x flag seems to do the job

  DB<113> $_="AAAA";  $c="A"; $min=3; /$c {$min}/x; $&
 => "AAA"
[download]

UPDATE

TIMTOWTDI

  DB<108> $c="A";$min=3
 => 3

  DB<109> "AAAAA" =~ m/${c}{$min}/;  $&
 => "AAA"
[download]