diff --git a/src/mesa/state_tracker/st_pbo_compute.c b/src/mesa/state_tracker/st_pbo_compute.c
index 449307359e0..b65a1ae787f 100644
--- a/src/mesa/state_tracker/st_pbo_compute.c
+++ b/src/mesa/state_tracker/st_pbo_compute.c
@@ -1304,11 +1304,12 @@ st_GetTexSubImage_shader(struct gl_context * ctx,
       return false;
 
    view_target = get_target_from_texture(src);
-   /* I don't know why this works
-    * only for the texture rects
-    * but that's how it is
-    */
-   if ((src->target != PIPE_TEXTURE_RECT &&
+
+   /* 64K x 64K aren't supported by the shader (pbo_data::width/height have 16 bits) */
+   if (width >= UINT16_MAX || height >= UINT16_MAX ||
+       /* I don't know why this works only for the texture rects
+        * but that's how it is. */
+       (src->target != PIPE_TEXTURE_RECT &&
        /* this would need multiple samplerviews */
        ((util_format_is_depth_and_stencil(src_format) && util_format_is_depth_and_stencil(dst_format)) ||
        /* these format just doesn't work and science can't explain why */