A methodology to estimate, in a probabilistic way, the annual cost to society of premature deaths because of earthquakes is proposed in this paper. The methodology makes use of results obtained by means of prospective and probabilistic seismic risk assessments where, expected deaths caused by the collapse of buildings are obtained. Those results, combined with demographic and macroeconomic indicators such as the age distribution, life expectancy at birth and per capita gross domestic product, are used to estimate the cost to society in terms of lost productivity due to premature mortality because of earthquakes. The proposed methodology does not attempt to estimate neither assign a cost to human lives at any stage, but the one associated to lost productivity at societal level. One of the descriptors of the methodology is part of the components of the disability adjusted lost years (DALY), a widely used metric in the public health field which estimates the burden of diseases based mostly on historical data. As an example, the methodology is applied to Medellín, the second largest city of Colombia, finding that the cost of lost productivity due to premature mortality because of earthquakes has a similar order of magnitude than the direct physical losses in the public and private building stock calculated in a previous probabilistic seismic risk assessment.