Background As in many countries worldwide, due to the COVID-19 pandemic lockdown, higher institutions in Nigeria closed in March 2020 and only began reopening in October of the same year. As a result of the lockdown, some higher institutions had to quickly move from the traditional face-to-face teaching method to virtual learning. This study aimed to investigate the impact of COVID-19 lockdown on education in Nigeria and also provide recommendations that may be useful in developing remote teaching contingency strategies. Five-point Likert-scale questionnaire targeting students and teachers separately was designed to get feedbacks from both students and teachers on their experiences, issues and successes. The questionnaires were divided into five categories: virtual classrooms, course learning outcomes, alternative method of assessment, impact of online teaching and satisfaction. Results A total of 703 students and 60 teachers from five different local universities participated in this study. All participants (> 50%) had difficulties with Internet connection. Students (67%) as well as teachers (59%) agree that they had limited interactions with one another and this negatively influence student’s satisfaction (p < 0.01). While students were split on the most appropriate method of assessment, teachers (63%) believe assignments and oral examinations are more suitable for online teaching. Many teachers (66%) admitted that it was difficult assessing students’ abilities and performance. Some students (> 40%) were concerned about the number of assignments given. Most teachers (84%) believe there is an increase in tendency for examination malpractice when assessment was conducted virtually. Students had significantly (p < 0.05) higher marks in all courses during online assessment compared to previous session involving face-to-face teaching. About 83% of teachers admitted it was difficult explaining complex scientific concepts. Conclusion Based on the results of this study, we provided recommendations to help educational institutions in Nigeria develop remote teaching contingency strategies.