See TIME AND DATE FUNCTIONS in Excel::Writer::XLSX::Utility. Assuming all cells in column T are dates.

#!/usr/bin/perl 
use strict;
use Excel::Writer::XLSX;
use Excel::Writer::XLSX::Utility;
use DBI;
my $dbh = get_dbh(); # connect as req

my $workbook = Excel::Writer::XLSX->new( 'perl.xlsx' );
my $worksheet = $workbook->add_worksheet();

# set column format
my $datecol = 19;
my $date_format = $workbook->add_format(num_format=>'m/d/yyyy h:mm');
$worksheet->set_column($datecol,$datecol,15,$date_format);#width 15

my $sql = "SELECT * FROM test21";
my $sth = $dbh->prepare($sql);
$sth->execute;

my $row2 = 1;
while (my $aref = $sth->fetchrow_arrayref){
 
  # convert to Excel date
  my $date = $aref->[$datecol];
  $date =~ s/ /T/; # optional
  print "$date\n";
  $aref->[$datecol] = xl_parse_date( $date );

  $worksheet->write_row($row2++,0,$aref);
}   
$workbook->close;
[download]