During outbreaks of hospital-acquired influenza-like illness (HA-ILI) healthcare workers (HCWs), patients, and visitors are each a source of infection for the other. Quantifying the effects of these various exposures will help improve prevention and control of HA-ILI outbreaks. We estimated the attributability of HA-ILI to: (1) exposure to recorded or unrecorded sources; (2) exposure to contagious patient or contagious HCW; (3) exposure during observable or unobservable contagious period of the recorded sources; and, (4) the moment of exposure. Among recorded sources, 59% [95% credible interval (CrI) 34–83] of HA-ILI of patients was associated with exposure to contagious patients and 41% (95% CrI 17–66) with exposure to contagious HCWs. Exposure during the unobservable contagiousness period of source patients accounted for 49% (95% CrI 19–75) of HA-ILI, while exposure during the unobservable contagiousness period of source HCWs accounted for 82% (95% CrI 51–99) of HA-ILI. About 80% of HA-ILIs were associated with exposure 1 day earlier. Secondary cases of HA-ILI might appear as soon as the day after the detection of a primary case highlighting the explosive nature of HA-ILI spread. Unobservable transmission was the main cause of HA-ILI transmission suggesting that symptom-based control measures alone might not prevent hospital outbreaks. The results support the rapid implementation of interventions to control influenza transmission.