A filter fault detection apparatus for a filter mounted on an exhaust passage of an internal combustion engine for collecting particulate matter includes a sensor mounted on the exhaust passage downstream of the filter. The sensor includes an insulative sensor element formed with a pair of electrodes on which particulate matter is collected, the sensor generating a sensor output corresponding to an amount of particulate matter collected on the sensor element when the electrodes become electrically conductive therebetween, causing the sensor output to rise. The apparatus further includes an acquiring unit that acquires, as an output variation, a temporal variation of the sensor output after rise of the sensor output, and a fault determination unit that performs a fault detection process for detecting presence of a fault in the filter based on the output variation of the sensor output to determine whether the filter is normal or faulty.