The timing of the injury is particularly cruel for the youngster, who has become a focal point of the Selecao's attack under Ancelotti.
Prior to this setback, Estevao was considered a certainty to make the final squad for the tournament in North America, with Ancelotti frequently praising the winger's impact since his international debut.
Brazil are scheduled to begin their World Cup campaign against Morocco on June 13, leaving Estevao with a dwindling window to regain match fitness.
The five-time world champions have been drawn in Group C, where they will also face challenges from Morocco, Scotland and Haiti as they look to secure their first global title since 2002.