Determining when to throttle interrupts to limit interrupt processing to an interrupt processing time period

Provided are a computer program product, system, and method for determining when to throttle interrupts to limit interrupt processing to an interrupt processing time. Upon receiving interrupts from the hardware device, a determination is made as to whether a number of received interrupts exceeds an interrupt threshold during a interrupt tracking time period. If so, an interrupt throttling state is set to a first value indicating to only process interrupts during an interrupt processing time period. Interrupts from the hardware device are processed during the interrupt time period when the interrupt throttling state is set to the first value. Interrupts received from the hardware are masked during a processing of a scan loop of operations while the interrupt throttling has the first value and the interrupt processing time period has expired, wherein the masked interrupts are not processed while processing the scan loop of operations.