A cell image analysis apparatus comprising: a threshold value storage unit configured to store a cell nucleus threshold value, a fragmented cell nucleus threshold value, and a cell nucleus area threshold value in advance; an image input unit configured to input a cell image captured from a cell stained with a fluorescent substance; a cell nucleus region extraction unit configured to extract, from the input cell image, a region having an area equal to or larger than the cell nucleus area threshold value from among regions having a luminance value equal to or larger than the cell nucleus threshold value as a cell nucleus region and to acquire information representing the position and range of the cell nucleus region; a fragmented cell nucleus region extraction unit configured to extract, from the cell nucleus region, a region having a luminance value equal to or larger than the fragmented cell nucleus threshold value as a fragmented cell nucleus region and to acquire information representing the position and range of the fragmented cell nucleus region; wherein the fragmented cell nucleus region extraction unit includes a candidate region extraction unit configured to extract, from the cell nucleus region, a region having a luminance value equal to or larger than the fragmented cell nucleus threshold value as a candidate region, and a region determination unit configured to perform boundary detection processing based on the gradient of the luminance value of each pixel to detect a boundary in the candidate region, and extract a region surrounded by the detected boundary as the fragmented cell nucleus region; and an analysis result output unit configured to output an analysis result on the basis of information representing the positions and ranges of the cell nucleus region and the fragmented cell nucleus region respectively extracted from the cell nucleus region extraction unit and the fragmented cell nucleus region extraction unit, wherein the analysis result output unit is configured to output at least the number of fragmented cell nucleus regions. a threshold value storage unit configured to store a cell nucleus threshold value, a fragmented cell nucleus threshold value, and a cell nucleus area threshold value in advance; an image input unit configured to input a cell image captured from a cell stained with a fluorescent substance; a cell nucleus region extraction unit configured to extract, from the input cell image, a region having an area equal to or larger than the cell nucleus area threshold value from among regions having a luminance value equal to or larger than the cell nucleus threshold value as a cell nucleus region and to acquire information representing the position and range of the cell nucleus region; a fragmented cell nucleus region extraction unit configured to extract, from the cell nucleus region, a region having a luminance value equal to or larger than the fragmented cell nucleus threshold value as a fragmented cell nucleus region and to acquire information representing the position and range of the fragmented cell nucleus region; wherein the fragmented cell nucleus region extraction unit includes a candidate region extraction unit configured to extract, from the cell nucleus region, a region having a luminance value equal to or larger than the fragmented cell nucleus threshold value as a candidate region, and a region determination unit configured to perform boundary detection processing based on the gradient of the luminance value of each pixel to detect a boundary in the candidate region, and extract a region surrounded by the detected boundary as the fragmented cell nucleus region; and a candidate region extraction unit configured to extract, from the cell nucleus region, a region having a luminance value equal to or larger than the fragmented cell nucleus threshold value as a candidate region, and a region determination unit configured to perform boundary detection processing based on the gradient of the luminance value of each pixel to detect a boundary in the candidate region, and extract a region surrounded by the detected boundary as the fragmented cell nucleus region; and an analysis result output unit configured to output an analysis result on the basis of information representing the positions and ranges of the cell nucleus region and the fragmented cell nucleus region respectively extracted from the cell nucleus region extraction unit and the fragmented cell nucleus region extraction unit, wherein the analysis result output unit is configured to output at least the number of fragmented cell nucleus regions.