diff --git a/src/core/Core.js b/src/core/Core.js
index 6027f1bee..537ac9a38 100644
--- a/src/core/Core.js
+++ b/src/core/Core.js
@@ -389,7 +389,13 @@ class Uppy {
       .catch((err) => {
         const message = typeof err === 'object' ? err.message : err
         this.info(message, 'error', 5000)
-        return Promise.reject(typeof err === 'object' ? err : new Error(err))
+        const rejected = Promise.reject(typeof err === 'object' ? err : new Error(err))
+        // Silence the unhandled rejection; we have already shown it to the user,
+        // so the consumer may not need to do anything with this result.
+        // Note that the result is still a rejected Promise, it will just not
+        // trigger unhandled rejection warnings in the browser console.
+        rejected.catch(() => {})
+        return rejected
       })
   }