Coronavirus disease (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has caused a rapidly spreading pandemic and is severely threatening public health globally. The human-to-human transmission route of SARS-CoV-2 is now well established. The reported clinical observations and symptoms of this infection in humans appear in the range between being asymptomatic and severe pneumonia. The virus can be transmitted through aerosols and droplets that are released into the air by a carrier, especially when the person coughs, sneezes, or talks forcefully in a closed environment. As the disease progresses, the use and handling of contaminated personal protective equipment and facemasks have become major issues with significant environmental risks. Therefore, providing an effective method for treating used/contaminated facemasks is crucial. In this paper, we review the environmental challenges and risks associated with the surge in facemask production. We also discuss facemasks and their materials as sources of microplastics and how disposal procedures can potentially lead to the contamination of water resources. We herein review the potential of developing nanomaterial-based antiviral and self-cleaning facemasks. This review discusses these challenges and concludes that the use of sustainable and alternative facemask materials is a promising and viable solution. In this context, it has become essential to address the emerging challenges by developing a new class of facemasks that are effective against the virus, while being biodegradable and sustainable. This paper represents the potentials of natural and/or biodegradable polymers for manufacturing facemasks, such as wood-based polymers, chitosan, and other biodegradable synthetic polymers for achieving sustainability goals during and after pandemics.