APOBEC3 enzymes are cytosine deaminases implicated in cancer. Precisely when APOBEC3 expression is induced during cancer development remains to be defined. Here we show that specific APOBEC3 genes are upregulated in breast DCIS, and in pre-invasive lung cancer lesions coincident with cellular proliferation. We observe evidence of APOBEC3-mediated subclonal mutagenesis propagated from TRACERx pre-invasive to invasive NSCLC lesions. We find that APOBEC3B exacerbates DNA replication stress and chromosomal instability through incomplete replication of genomic DNA, manifested by accumulation of mitotic ultrafine bridges and 53BP1 nuclear bodies in the G1 phase of the cell cycle. Analysis of TRACERx NSCLC clinical samples and mouse lung cancer models, revealed APOBEC3B expression driving replication stress and chromosome missegregation. We propose that APOBEC3 is functionally implicated in the onset of chromosomal instability and somatic mutational heterogeneity in pre-invasive disease, providing fuel for selection early in cancer evolution.