In 2021–2022, influenza vaccine coverage in the US dropped below pre-COVID-19 pandemic levels. Cocirculation of COVID-19 and influenza could place a substantial burden on hospital utilization in future seasons, particularly given the reduced exposure to influenza during the pandemic. We used a dynamic susceptible-exposed-infected-recovered model to simulate influenza transmission with varying influenza vaccine coverage against a background of COVID-19 circulation, in order to estimate acute and ICU hospital bed occupancy for both diseases. We evaluated two vaccine scenarios: egg-based quadrivalent influenza vaccine (QIVe) for all age groups or cell-based QIV (QIVc) for 0.5–64 year-olds with adjuvanted QIV (aQIV) for ≥65 year-olds. ICU bed availability was more limiting than general hospital bed availability, with a vaccine coverage of ≥70% required to avoid negatively impacting ICU bed availability in a high-incidence influenza season. The timing of disease peaks was a key factor together with vaccine coverage, with a difference of ≥50 days needed between peak influenza and COVID-19 bed usage together with 65% influenza vaccine coverage to avoid negative impacts. QIVc + aQIV resulted in lower bed occupancy which, while not substantial, may be critical in very high hospital resource usage situations. In a situation with co-circulating influenza and COVID-19, proactive vaccination planning could help to avert overwhelming healthcare systems in upcoming influenza seasons.