Provenance is a record that describes how entities, activities, and agents have influenced a piece of data; it is commonly represented as graphs with relevant labels on both their nodes and edges. With the growing adoption of provenance in a wide range of application domains, users are increasingly confronted with an abundance of graph data, which may prove challenging to process. Graph kernels, on the other hand, have been successfully used to efficiently analyse graphs. In this paper, we introduce a novel graph kernel called provenance kernel, which is inspired by and tailored for provenance data. It decomposes a provenance graph into tree-patterns rooted at a given node and considers the labels of edges and nodes up to a certain distance from the root. We employ provenance kernels to classify provenance graphs from three application domains. Our evaluation shows that they perform well in terms of classification accuracy and yield competitive results when compared against existing graph kernel methods and the provenance network analytics method while more efficient in computing time. Moreover, the provenance types used by provenance kernels also help improve the explainability of predictive models built on them.