The 40-year-old midfielder picked up the injury in Sunday's goalless match and was substituted during the second half after taking a heavy blow to the left side of his face. AC Milan later confirmed that Modric would undergo surgery, while Croatia also released a statement on the injury ahead of the summer tournament.
Despite the setback, Croatia manager Zlatko Dalic remained confident that his captain would recover in time for the opening Group L clash against England on June 11 in Arlington, Texas.
Dalic revealed he had already spoken with the veteran playmaker and backed him to do everything possible to return quickly.
"I've been talking to Luka and wished him a successful surgery and a speedy recovery," Dalic said.
"I am convinced that he will do everything to be ready for the World Cup, and we will provide him with full support."
The Croatia boss also expressed confidence that Modric would recover as planned and continue leading the national team on football's biggest stage.
"I am confident that the recovery will go according to plan and that Luka, as team captain, will lead us at another major competition this summer," he added.
There is a possibility Modric could wear a protective face mask if he is cleared to play against England. Croatia's remaining group matches are against Panama on June 24 and Ghana on June 27.
The former Real Madrid star is aiming to appear at his fifth World Cup. Modric captained Croatia to the 2018 World Cup final in Russia, where they finished runners-up after losing to France, and he later won the Ballon d'Or that same year.