The 21-year-old joined the Monaco youth system from Aix-en-Provence in 2007 and went on to make his professional debut in September 2010.
Despite Monaco having spent millions this summer, Kurzawa is a homegrown player with plenty of potential.
Kurzawa told the club's official website: "I am very pleased with the confidence that the club has shown in me.
"It was very important for me to continue to learn in my club and in this fantastic project with a coach like Claudio Ranieri who has confidence in me and with experienced players around me."
Vice-president Vadim Vasilyev added: "As we have explained, it is essential for us to keep our promising young players."