Short tandem repeats (STRs) are hotspots of genomic variability in the human germline because of their high mutation rates, which have long been attributed largely to polymerase slippage during DNA replication. This model suggests that STR mutation rates should scale linearly with a father's age, as progenitor cells continually divide after puberty. In contrast, it suggests that STR mutation rates should not scale with a mother's age at her child's conception, since oocytes spend a mother's reproductive years arrested in meiosis II and undergo a fixed number of cell divisions that are independent of the age at ovulation. Yet, mirroring recent findings, we find that STR mutation rates covary with paternal and maternal age, implying that some STR mutations are caused by DNA damage in quiescent cells rather than polymerase slippage in replicating progenitor cells. These results echo the recent finding that DNA damage in oocytes is a significant source of de novo single nucleotide variants and corroborate evidence of STR expansion in postmitotic cells. However, we find that the maternal age effect is not confined to known hotspots of oocyte mutagenesis, nor are postzygotic mutations likely to contribute significantly. STR nucleotide composition demonstrates divergent effects on de novo mutation (DNM) rates between sexes. Unlike the paternal lineage, maternally derived DNMs at A/T STRs display a significantly greater association with maternal age than DNMs at G/C-containing STRs. These observations may suggest the mechanism and developmental timing of certain STR mutations and contradict prior attribution of replication slippage as the primary mechanism of STR mutagenesis.