You can want to add 'M' and '_' in parens to capture in one shot or concatanate 'M'.$1.'_' depending of what you want to do. One way to do it:

#!/usr/bin/perl -w
use strict;

my $seqnum=1;
while (my $seq=<DATA>) {
    chomp $seq;
    print "sequence #",$seqnum++,":\n";
    while ($seq =~ /M([GAVLIFWPSTCYNQDEKRH]+)_/g) {
        print "\t",$1,"\n";
        # or: print "\t","M${1}_","\n";
    }
    
}

__DATA__
MHGRRRRRRRRRRRRRRRRRRRRRRRRRRRRRD_MHGRRRRRRRRD_
CMAAAAAAAAAAAAAAAAAAAAAAAAAAAAAVTECMAAAAAAAAAAAAAAAAAAAAAAAAAAAAAVT
AWPPPPPPPPPPPPPPPPPPPPPPPPPPPPP_LNAWPPPPPPPPPPPPPPPPPPPPPPPPPPPPP_L
FOOBARMNOTTHISONE_XYZMTHISYES_MTHISNOT_
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