In this paper, we introduce almost Suzuki type $\mathcal{Z}_s$-contractions and prove the existence and uniqueness of fixed points of such mappings in complete $S$-metric spaces. Our results generalize Theorem 1 from [N. Mlaiki, N. Yılmaz Özgür, Nihal Taş, Mathematics, 7 (583) 2019, 12 pages] and Theorem 3.1 from [S. Sedghi, N. Shobe, A. Aliouche, Mat. Vesnik, 64 (3) (2012), 258-266]. We give illustrative examples in support of our result.