Schlafen 11 (SLFN11) is an interferon-inducible antiviral restriction factor with tRNA endoribonuclease and DNA binding functions. It is recruited to stalled replication forks in response to replication stress and inhibits replication of certain viruses such as the human immunodeficiency virus 1 (HIV-1) by modulating the tRNA pool. SLFN11 has been identified as a predictive biomarker in cancer, as its expression correlates with a beneficial response to DNA damage inducing anticancer drugs. However, the mechanism and interdependence of these two functions are largely unknown. Here, we present cryo-electron microscopy (cryo-EM) structures of human SLFN11 in its dimeric apoenzyme state, bound to tRNA and in complex with single-strand DNA. Full-length SLFN11 neither hydrolyses nor binds ATP and the helicase domain appears in an autoinhibited state. Together with biochemical and structure guided mutagenesis studies, our data give detailed insights into the mechanism of endoribonuclease activity as well as suggestions on how SLFN11 may block stressed replication forks.