(1) Background: To assess the time trend in the prevalence of chronic neck pain (CNP), chronic low back pain (CLBP), and migraine or frequent headache (MFH) among people with diabetes in Spain from 2014 to 2020, this study identified sex differences and compared the prevalence of these pain sites between people with diabetes and age-sex-matched non-diabetic subjects. (2) Methods: The study design included a cross-sectional and a case-control study. The data were obtained from the European Health Interview Surveys for Spain conducted in 2014 and 2020. The presence of diabetes, CNP, CLBP, and MFH was self-reported. Study covariates included sociodemographic characteristics, comorbidities, lifestyles, and pain-related variables. (3) Results: Among people with diabetes, the prevalence of CNP, CLBP, and MFH did not improve from 2014 to 2020. Women with diabetes had a significantly higher prevalence of all the pain sites analyzed than men with diabetes. After matching by sex and age, the prevalence of CNP (26.0% vs. 21.1%; < 0.001), CLBP (31.2% vs. 25.0%; < 0.001), and MFH (7.7% vs. 6.5%; = 0.028) was higher for people with diabetes than for those without diabetes. Self-reported mental disease was independently associated with reporting the three pain sites analyzed in people with diabetes. (4) Conclusions: The prevalence of CNP, CLBP, and MFH has remained stable over time. Remarkable sex differences were found, with a higher prevalence among women than men with diabetes. Diabetes was associated with reporting in all the pain sites analyzed. Self-reported mental disease was associated with reporting CNP, CLBP, and MFH.