Infectious mononucleosis (IM) often results from late primary infection with Epstein–Barr virus (EBV). Exposure to EBV at ages 0–2 years from, e.g., siblings therefore protects against IM. Using Danish registers, we therefore followed children born in 1997 through 2015 from age 3 years for a hospital contact with an IM diagnosis as outcome with the number of antimicrobial prescriptions filled before age 3 years as a proxy of infection pressure and the main exposure in stratified Cox regressions. The main analyses used sibships as strata primarily to adjust for health-seeking behaviour with further possible adjustments for age, sex, calendar period and sibship constellation. In these analyses we followed 7087 children, exposed on average to 3.76 antimicrobials prescriptions. We observed a crude hazard ratio for IM per unit increase in cumulative antimicrobial use of 1.00 (95% confidence interval 0.99, 1.02), with similar results in adjusted analyses. The hypothesis that children with the largest use of antimicrobials at ages 0–2 years would subsequently have the lowest risk of IM within a sibship was not corroborated by the data. Furthermore, sibship-matched analyses provided no support for some common early-life immune system characteristics being predictive of IM.