The softwarization and virtualization based Network Slicing (NS) technology provides the momentum for integrating the Information-Centric Networking (ICN) systems into the 5G infrastructure, such that ICN can be virtualized as a NS to co-exist with other IP-based vertical services slices. The implementation of the ICN network slice (ICN-NS) is essentially a 5G end-to-end (E2E) NSs embedding problem, which is normally solved by embedding the given virtual network (VN) of the slice instance. However, determining the details of the VN is non-trivial and largely ignored in the literature. In this work, we formulate the ICN network slices determination and embedding (ICN-NS-DE) problem through an Integer Linear Program (ILP) formulation, such that the ICN-NS determination and embedding problems are jointly solved for a hierarchical ICN system without requiring a-priori knowledge on the VN's topology and resource provisioning information. Due to the complexity of the model, we design an heuristic algorithm for solving the problem in practical large scale network. Finally, we demonstrate the performance of the ICN-NS-DE model and the algorithm through intensive simulations.