Make the figure tag an inline-block and assign has-text-centered to the parent tag. Advantage is no custom code needed.
<link href="https://cdnjs.cloudflare.com/ajax/libs/bulma/0.6.2/css/bulma.min.css" rel="stylesheet"/>
<div class="column is-one-quarter">
<div class="card equal-height">
<div class="card-image has-text-centered">
<figure class="image is-64x64 is-inline-block">
<img class="is-rounded" src="https://unsplash.it/64"/>
</figure>
</div>
<div class="card-content">
<!-- other content here -->
</div>
</div>
</div>