An Amazon spokesperson told CNBC that the company requests safety documentation "very shortly" after a product is listed by a third party seller. In an email statement, the company said it regularly contacts selling partners to request safety documentation. Sellers who do not provide the required documentation are removed immediately.

That practice leaves a window in which unsafe toys could potentially be sold to consumers. To make matters worse, Amazon recently came under fire for selling thousands of items that federal agencies had deemed unsafe. After a Wall Street Journal investigation discovered everything from unregistered pesticides to banned toys on the site, three senators wrote a letter asking Amazon CEO Jeff Bezos to launch a "sweeping internal investigation" into the company's safety policies. It's unclear if Amazon has taken any steps since then to improve consumer safety, but now, it will likely be under increased pressure to do so.