I'm using MDBootstrap 4.8.5, and I have this working.

var input = $('#autocomplete').val();
var options = function() {
    var returned_info = null;
    $.ajax({
        method: 'POST',
        url: 'your/ajax/script.php',
        data: 'input=' + input,
        dataType: 'json', // expect a JSON response
        async: false,
        global: false,
        success: function(data) {
            returned_info = data;
        }
    });
    return returned_info;
}();
$('input#autocomplete').mdbAutocomplete({
    data: options
});

Your PHP script should look something like:

<?php
// DB Connection Info

header( 'Content-Type: application/json' );

$input = trim($_REQUEST['input']);
$input = strval($input);
$input = filter_var( $input, FILTER_SANITIZE_STRING );

if ( isset( $input ) ) {
  $input = $input . '%';

  $stmt = $conn->prepare( "SELECT [column(s)] FROM [table(s)] WHERE [column(s) have] LIKE :input" );
  $stmt->bindParam( ':input', $input );
  $stmt->execute();

  if ( $stmt->rowCount() > 0 ) {
    while ( $row = $stmt->fetch( PDO::FETCH_ASSOC ) ) {
      $country_result[] = $row['name']; 
    }
    print(json_encode($country_result)); // returns results as JSON which is what your AJAX is expecting
  } else {
    // having trouble converting this to JSON personally
    //echo( '<p class="text-center">No Results Found!</p>' );
  }
}

$stmt = null;
$conn = null;
?>