This paper describes two locally-differential private algorithms for releasing user vectors such that the Jaccard similarity between these vectors can be efficiently estimated. The basic building block is the well known MinHash method. To achieve a privacy-utility trade-off, MinHash is extended in two ways using variants of Generalized Randomized Response and the Laplace Mechanism. A theoretical analysis provides bounds on the absolute error and experiments show the utility-privacy trade-off on synthetic and real-world data. A full version of this paper is available at http://arxiv.org/abs/2008.08134.