"Andrej is an extremely prolific striker who will add impetus to our attacking game," Hoffenheim football director Alexander Rosen told the club website.
Kramaric joined Leicester in January 2015 for a club record 9 million pounds from Croatia's Rijeka and he scored two league goals to help them avoid relegation with a late-season rally.
He has played nine times for Croatia and will hope his move to the Bundesliga earns him a place in the national squad for this year's European Championship in France.
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“Andrej has the European Championships to think about this summer, so it’s important for him that he has the opportunity to play," said Leicester manager Claudio Ranieri.
"I spoke with him to understand what he wants to do and a loan is a solution that works for everybody. We will watch him closely at Hoffenheim," the Italian told Leicester's website (www.lcfc.co.uk).
(Reporting by Ed Osmond; editing by Justin Palmer)
