Yes, you can request your supplier to ship your products directly to Amazon FBA. There are few things that you need to consider:

• Educating your supplier: Nowadays many suppliers are familiar with Amazon FBA process but still you may need to educate them with the process and explain to them that you need your inventory sent to Amazon warehouse directly. Some manufacturer, won’t do shipping for you and you may need to hire separate entity to do that.
• Choice between UPC/FNSKU: Every product sold on Amazon has a FNSKU code associated with it. Either you can get your supplier to paste FNSKU labels on your inventory items or have Amazon do it for you (extra charged by Amazon). If your supplier is doing it for you, then you need to make sure that they paste FNSKU code on top of UPC code (if your product has one) as your product shouldn’t have 2 barcodes. If you’re planning to sell outside Amazon, then you need UPC code.
• Additional Labeling Cost: Most of the supplier would do this for free but few may charge extra cents to do this. Please do compare the cost with Amazon labeling (.10 cents per unit). As Desmond suggested below, make sure to get the photos of product with labeling before it’s sent to Amazon FBA.
• Quality Check: If it’s a new supplier and you don’t have an old relationship with them, then you would definitely want to do a quality check of the product inventory before it’s sent to Amazon FBA warehouse. Poor quality of products will result in negative reviews and returns. If you’re a new seller, you can have your initial order sent to you or a freight forwarder who does the quality check. Post quality check, you can send the product to Amazon.
• Additional Shipping Cost for different warehouses: When supplier provides you the invoice, usually shipping cost is for one destination only. If you’ve multiple boxes of your inventory, Amazon’s system may want you to send your product to different warehouses. Shipping to different warehouses, may increase your shipping cost.