The 31-year-old, who joined the Brazilian side in 2019, went down after a challenge during the first half of Wednesday's Group A clash and had to be substituted.
"Arrascaeta... was taken to hospital, where a fracture to his right collarbone was confirmed," Flamengo wrote on their website.
Defending champions Flamengo remain top of the group with seven points from three matches.
Uruguay begin their World Cup campaign on June 15th with a Group H game against Saudi Arabia, leaving Arrascaeta with about six weeks to recover.