The bivariate sinc-Gauss sampling formula is introduced in Asharabi and Prestin (IMA J. Numer. Anal. 36:851–871, 2016) to approximate analytic functions of two variables which satisfy certain growth condition. In this paper, we apply this formula to approximate partial derivatives of any order for entire and holomorphic functions on an infinite horizontal strip domain using only finitely many samples of the function itself. The rigorous error analysis is carried out with sharp estimates based on a complex analytic approach. The convergence rate of this technique will be of exponential type, and it has a high accuracy in comparison with the accuracy of the bivariate classical sampling formula. Several computational examples are exhibited, demonstrating the exactness of the obtained results.