This is actually a very popular question / answer. Starting with Highcharts V2.2, you can assign "showEmpty: false" to define the y axis, and this ensures that when hiding, the text label of the Y axis will also be hidden. Example configuration snippet below:
yAxis: [{
min: 0,
showEmpty: false,
labels: {
formatter: function() {
return this.value;
},
style: {
color: '#3366CC'
}
},
title: {
text: 'Clicks',
style: {
color: '#3366CC'
}
},
id: 'Clicks'
},
...
, showEnabled = false , min, max. , min, , Highcharts V3.0.5