This year saw "the best holiday ever for the Kindle family as customers purchased millions of Kindle Fires and millions of Kindle e-readers," the Seattle-based online retail giant said.
Amazon said the Kindle Fire has been the "number one best-selling, most gifted and most wished for product" on Amazon.com since it went on sale 13 weeks ago.
Besides the Kindle Fire, Amazon offers a range of Kindle electronic book readers.
Amazon said it sold "well over" one million Kindle devices per week in December with the Kindle Touch and basic Kindle taking the top two spots after the Fire.
Amazon said the Kindle is its best-selling item in Britain, France, Germany, Italy and Spain in addition to the United States.
The company said "gifting" of Kindle books between November 25 and Christmas Day rose 175% compared to the holiday period last year with Christmas Day the biggest day ever for Kindle book downloads.
Despite the rosy sales numbers for the gadgets, Goldman Sachs said in a research note that the online titan may fall short of fourth-quarter earnings expectations.
Industry tracker comScore found that US online spending for the first 56 days of the November-December holiday season rose 15% over the same period last year to $35.3bn.
"On average, Amazon's year-over-year sales growth in the fourth quarter has outpaced holiday season eCommerce by 23 points," Goldman Sachs said.
"As such, the comScore data released today would imply top line growth of 38% year-over-year to $17.87bn, slightly below current consensus of $18.19bn, up 40% year-over-year."
The Kindle Fire costs $199, less than half the price of the cheapest iPad from tablet market leader Apple.
It has a seven-inch (17.78cm) screen, smaller than the iPad's 9.7 inches (24.6cm), connects to the web using wi-fi and is powered by Google's Android software.
It does not have a camera or the 3G connectivity featured on other tablets but gives buyers easy access to Amazon's online store, which sells books, music, movies, television shows, games and other content.