Providing a normal diet to a care recipient who is unable to form an adequate bolus may cause suffocation or aspiration pneumonia. We investigated whether differences in kinematic data of mandibular movements during mastication can be used as an indicator of the need for a dysphagia diet in the elderly in long-term care facilities. We included 63 participants who were provided with solid food in two long-term care facilities. The primary outcome variable was the kinematic data on mandibular movement during cracker chewing. The analysis results were compared between the normal and dysphagia diet groups. Logistic regression analysis and receiver operating characteristic curve analyses were performed. Significant differences were observed in the masticatory time, cycle frequency, total change amount, number of linear motions, and circular motion frequency between the normal and modified diet groups. The odds ratio for the circular motion frequency was −0.307, and the calculated cutoff value was 63%, with a sensitivity of 71.4%, a specificity of 73.5%, and an area under the curve of 0.714. Thus, these characteristics may be useful for detecting care recipients who need to be provided with a dysphagia diet. Moreover, the circular motion frequency could be used as a screening test to identify people who need a dysphagia diet.