Edit in JSFiddle

$(function() {
  (function(H) {
    H.wrap(H.Axis.prototype, 'drawCrosshair', function(proceed) {
      var axis = this;
      wasRendered = !!axis.cross; // on init, cross is not defiend
      proceed.apply(axis, Array.prototype.slice.call(arguments, 1));

      if (!wasRendered && axis.cross && axis.options.clickOnCrosshair) {
        axis.cross.on('click', function(e) {
          var point = axis.chart.hoverPoint;
          axis.options.clickOnCrosshair(e, point);
        });
      }

    });
  })(Highcharts);


  Highcharts.chart('container', {
    title: {
      text: 'Monthly Average Temperature',
      x: -20 //center
    },
    subtitle: {
      text: 'Source: WorldClimate.com',
      x: -20
    },
    xAxis: {
      categories: ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun',
        'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'
      ],
      clickOnCrosshair: function(e, p) {
        alert('Click on ' + p.category + ' category!')
        console.log(this, e, p);
      },
      crosshair: {
        enabled: true
      }
    },
    yAxis: {
      title: {
        text: 'Temperature (°C)'
      },
      plotLines: [{
        value: 0,
        width: 1,
        color: '#808080'
      }]
    },
    tooltip: {
      valueSuffix: '°C'
    },
    legend: {
      layout: 'vertical',
      align: 'right',
      verticalAlign: 'middle',
      borderWidth: 0
    },
    series: [{
      name: 'Tokyo',
      data: [7.0, 6.9, 9.5, 14.5, 18.2, 21.5, 25.2, 26.5, 23.3, 18.3, 13.9, 9.6]
    }, {
      name: 'New York',
      data: [-0.2, 0.8, 5.7, 11.3, 17.0, 22.0, 24.8, 24.1, 20.1, 14.1, 8.6, 2.5]
    }, {
      name: 'Berlin',
      data: [-0.9, 0.6, 3.5, 8.4, 13.5, 17.0, 18.6, 17.9, 14.3, 9.0, 3.9, 1.0]
    }, {
      name: 'London',
      data: [3.9, 4.2, 5.7, 8.5, 11.9, 15.2, 17.0, 16.6, 14.2, 10.3, 6.6, 4.8]
    }]
  });
});

<div id="container" style="min-width: 310px; height: 400px; margin: 0 auto"></div>