In this paper, we present a novel approach for the abstraction of monotone systems with bounded disturbances. The approach is data-driven and uses a given set of samples of the (unknown) dynamics of the system to compute an abstraction defined on partitions of the state and input spaces. The proposed method is efficient as its computational complexity is linear in the number of samples and in the size of the partitions. Moreover, the abstraction is shown to be minimally conservative in the absence of disturbances. We show that the resulting symbolic model is itself a monotone transition system and is related to the original system by an alternating simulation relation. We present some numerical experiments to show the effectiveness of the approach and to show how the choice of the partitions or the number of samples affects the quality of the approximation.