Subjective cognitive complaints (SCCs) are a crucial modifiable risk factor for dementia. There is increasing interest in the association between SCC and sleep disturbance; however, the effects of sleep disturbance on SCC development among community-dwelling elderly individuals in Japan remain unclear. We aimed to cross-sectionally investigate the association between SCC and sleep disturbance, with adjustment for multiple factors related to cognitive decline, among 241 community-dwelling elderly persons without cognitive impairment. The measures were SCCs (Kihon Checklist-Cognitive Function, KCL-CF), sleep disturbance (Japanese version of the Athens Insomnia Scale, AIS-J), general cognitive function (Mini-Mental State Examination), and depressive symptoms (five-item version of the Geriatric Depression Scale [GDS-5]). The following data were collected: sex, age, educational history, whether the participants had visited a medical institution for diseases (hypertension, diabetes, hyperlipidemia, heart disease), and the presence/absence of established risk factors (hearing loss, history of head injury, drinking habits, smoking habits, social isolation, and physical inactivity and activity). Based on the KCL-CF, 96 and 145 participants were considered to have and lack SCCs, respectively. On logistic regression analysis, the AIS-J score and smoking history were significantly associated with SCCs. Our findings suggest that sleep disturbance is associated with SCC development among community-dwelling elderly people in Japan. Evaluating and managing sleep disturbances can be important in preventing SCCs and dementia.