The coronavirus disease 2019 (COVID-19) outbreak has created unprecedent challenges for healthcare systems worldwide. Oncology services have been reorganized to decrease the risk of nosocomial acquisition of SARS-CoV-2, but changes in treatment pathways and follow-up cancer care can result in patients receiving suboptimal or delayed care. Herein, we describe a cross-sectional nested cohort study conducted to evaluate delays in care for patients with head and neck cancer (HNC) in post-treatment follow-up or palliative care during the COVID-19 pandemic in Northeast Brazil and its impact on health outcomes. Information was extracted from medical records and supplemented by telephone interviews. We compared the following health outcomes: self-perception of anxiety or sadness, fear of COVID-19 infection, cancer-related complications during social isolation, self-medication, diagnosis of COVID-19, and death between patients with and without delayed cancer care. The Mann-Whitney U test was used to compare distributions of continuous variables and the Fisher exact test was used for categorical variables. Thirty-one HNC patients were included in the study, and no case of confirmed SARS-CoV-2 was found. Delayed cancer care due to restriction in health services was reported in 58.1% of cases, and there was no report of telemedicine use during the COVID-19 outbreak. Cancer-related complications during the COVID-19 pandemic were described for most patients (67.7%) and included pain or discomfort, swelling, and dyspnea. Eight (25.8%) patients reported use of prescribed morphine or codeine to manage pain and six (19.4%) patients reported self-medication with over-the-counter (OTC) non-steroidal anti-inflammatory drugs (NSAIDs). We found an association between delayed HNC care and the use of self-medication (p = 0.028). This study indicated that patients with delayed HNC care during the COVID-19 outbreak are more likely to use self-medication with NSAIDs for pain management. Better strategies to follow HNC patients in socioeconomically disadvantaged communities need to be discussed and implemented.