Horizontally transferred genetic elements such as viruses and conjugative plasmids move DNA between organisms, increasing genetic diversity but destabilizing engineered biological systems. Here, we used a genomically recoded Escherichia coli strain lacking UAG stop codons and the recognition protein release factor 1 to study how an alternative genetic code influences horizontally transferred genetic element propagation. The alternative genetic code conferred resistance to multiple viruses (λ, M13, P1, MS2) at titers up to 10(11) PFU/ml and impaired conjugative plasmids (F and RK2) up to 10(5)-fold. By recoding UAG codons to UAA in viruses and plasmids, we restored viral infectivity and conjugative function. Propagating viruses on a mixed community of cells with standard and alternative genetic codes reduced viral titer, and over time viruses adapted to the alternative genetic code. This work demonstrates that altering the genetic code broadly obstructs the propagation of horizontally transferred genetic elements and supports the use of genomic recoding as a strategy to stabilize engineered biological systems.