As long as the glacier’s surface has a slope, it can happen. An avalanche is simply the action of snow falling down a steep slope, and a lot of it all at once. While we tend to hear of avalanches more frequently on mountains, don’t discount a glacier. It can get in on the action if it wants to.
For example, Lirung Glacier had an avalanche in 2014. This glacier is located in Langtang Valley, Nepal. It’s in the Himalayan mountains, so there’s a possibility the avalanche started on a mountain, but nonetheless, the glacier had an avalanche!
There are other avalanches that have taken place on glaciers, but they aren’t as “exciting” for the news anchors to cover since hardly anyone lives close enough to a glacier to be in danger.