Welcome to Perl Monks.

The syntax problem with your code is that foreach runs a loop so you need to use it like this:

foreach (@vettore) { 
   print $_ . "\n";        
}
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But it looks like you may actually want to print the output to your filehandle $fh by replacing your print with print $fh "$_\n"

Perhaps this script will help show some other ideas

# The following two lines check your code and
# alert you to many common errors
use strict;
use warnings;

# Lets keep the filespec out the main code
# using my when defining a variable limits its scope. 
my $infile  = "rep_set_ass_tax.fna"; 
my $outfile = "seq_id.txt"; 

# No point going on if we can not open both files
# You were opening the outfile in a loop before, lots of opens
# and closes happening that were not needed
open my $in,  '<',  $infile  or die "Can't read $infile: $!\n"; 
open my $out, '>>', $outfile or die "Can't read $outfile: $!\n"; 

while (my $line=<$in>) { 
   if($line=~/^>/) {           # ^ added for only lines starting with 
+> 
      my @vettore=split(/\s+/, $line);  
      foreach (@vettore) {    # can use for(@array) but they are the s
+ame
         print $out "$_ \n"; # Variables can be interpolated in a stri
+ng
      }                       # end foreach loop    
   } 
} 
close $in;
close $out;
[download]

If you are going to post more often it may be worth having a look at how to format your posts :)

Cheers,
R.