Cas13 can be used for the knockdown, editing, imaging or detection of RNA and for RNA-based gene therapy. Here by using RNA immunoprecipitation sequencing, transcriptome profiling, biochemical analysis, high-throughput screening and machine learning, we show that Cas13 can intrinsically target host RNA in mammalian cells through previously unappreciated mechanisms. Different from its known cis/trans RNA-cleavage activity, Cas13 can also cleave host RNA via mechanisms that are transcript-specific, independent of the sequence of CRISPR RNA and dynamically dependent on the conformational state of Cas13, as we show for several Cas13-family effectors encoded in one-vector and two-vector lentiviral systems. Moreover, host genes involved in viral processes and whose transcripts are intrinsically targeted by Cas13 contribute to constraining the lentiviral delivery and expression of Cas13. Our findings offer guidance for the appropriate use of lentiviral Cas13 systems and highlight the need for caution regarding intrinsic RNA targeting in Cas13-based applications.