Something like:

$array[1]->{Contact} = [];

%hash = ( Contact_Tel  => '1234',
          Contact_Name => 'Mr. Bean');

push @{$array[1]->{Contact}}, \%hash;
[download]

$array[1]->{Contact} contains the reference to an empty array.
Since push requires a 'real' array as its first argument, you have to dereference the reference in $array[1]->{Contact}.
You do this with @{...}.

See: here and here for more.