This paper is concerned with online targeted advertising on social networks. The main technical task we address is to estimate the activation probability for user pairs, which quantifies the influence one user may have on another towards purchasing decisions. This is a challenging task because one marketing episode typically involves a multitude of marketing campaigns/strategies of different products for highly diverse customers. In this paper, we propose what we believe is the first tensor-based contextual bandit framework for online targeted advertising. The proposed framework is designed to accommodate any number of feature vectors in the form of multi-mode tensor, thereby enabling to capture the heterogeneity that may exist over user preferences, products, and campaign strategies in a unified manner. To handle inter-dependency of tensor modes, we introduce an online variational algorithm with a mean-field approximation. We empirically confirm that the proposed TensorUCB algorithm achieves a significant improvement in influence maximization tasks over the benchmarks, which is attributable to its capability of capturing the user-product heterogeneity.