The COVID-19 disease has caused a drastic stoppage in the construction industry as a result of quarantines. For this reason, this study focuses on the workforce scheduling problem when working under COVID labor distancing constraints, and additional costs derived from deviation hours or hiring new employees that managers must assume on a project due to circumstances. A multi-objective mixed integer linear programming model was developed and solved using weighting and epsilon constraint methods to evaluate workforce scheduling and the mentioned COVID costs. The first objective function corresponds to the sum of the total extra hours; the second objective function represents the total non-worked but paid hours. Two sets of experiments are presented, the first based on a design of experiments that seeks to determine the relationship between the proposed objective functions and a methodology to determine the cost of considering COVID constraints. The second set of experiments was applied in a real company, where the situation without COVID vs with COVID, and without allowing extra hours vs with COVID allowing extra hours were compared. Obtained results showed that hiring additional employees to the man-crew leads the company to increase the extra hours cost up to 104.25%, being more convenient to keep a workforce baseline and to pay extra hours costs. Therefore, the mathematical model could represent a potential tool for decision-making in the construction sector, regarding the effects of COVID-19 costs on workforce scheduling construction projects. Consequently, this work contributes to the construction industry by quantifying the impact of COVID-19 constraints and the associated costs, offering a proactive approach to address the challenges posed by the COVID-19 pandemic for the construction sector.