Very interesting question. The earliest novels were called picaresque in that they involved a roguish main character who travelled widely, survived by means of their wits alone, and preyed on those less clever than themselves. These novels contrast the idea of chivalry with the idea of pursuing adventure for its own sake. They were also episodic, which meant that they were based around a series of single episodes which had no relation to the rest of the action in the book (kind of like when you miss an episode of Friends it doesn't really matter to the overall plot of the show). Lazarillo de Tormes and Don Quixote are examples of picaresque novels.
Based on this definition, therefore, Robinson Crusoe doesn't really seem to have all the elements of a picaresque novel. It does focus on one man's experience, but we can hardly describe him as a rogue, and though he does survive by his wits and skill, he does not take advantage of Man Friday in any devious fashion. Also, it is not episodic - there is a clear plot that runs throughout the story. It therefore can be said to represent the development of the novel from picaresque into something more interesting.
While Robinson Crusoe shares elements of the picaresque novel in that it is a first-person narrative that depicts a character living by his wits, it is not, in the end, of that genre. A picaresque character lives in and interacts with his society, and these interactions are often satiric, pointing out problems and vices in the larger culture. The hero often is the victim of cartoonish violence or caught in exaggerated situations. In contrast, Robinson Crusoe is almost always alone on his deserted island, first with animals and much later with Friday as his only companion, and his situation and survival are always realistically portrayed. While the novel is not without satiric moments, especially when Crusoe and Friday finally get to Europe, this book is largely an earnest account of one man's resourceful struggle to survive.
Further, a picaresque novel is usually a loose collection of somewhat disconnected episodes, whereas Crusoe has a tight trajectory of shipwreck, survival, and deliverance that unfolds as a whole. Finally, characters in a picaresque novel tend not to change, whereas Crusoe experiences growth, particularly in religious faith, as he survives on his island and has time to reflect on providence.