Havili limped off in the Crusaders' 42-18 home win over the Waratahs on Saturday and will miss the Rugby Championship and the remaining rounds of the Super Rugby Pacific season.
The Rugby World Cup starts on September 8 when New Zealand play hosts France in the opening match.
Robertson, who will take over as All Blacks head coach early next year, said Havili will miss between six and eight weeks.
"I'm sure he can (be fit), it'll only be a matter of weeks (out)," Robertson said of Havili's World Cup prospects.
Havili has played 25 Tests. His last appearance for New Zealand was a 25-all draw against England at Twickenham in November.
He will however be absent when New Zealand kick off their Rugby Championship campaign away to Argentina on July 8.
The All Blacks then play reigning world champions South Africa the following week in Auckland.
Havili was added to the Crusaders' injury list alongside loose forward Cullen Grace, who suffered a dislocated knee in the same game. Grace won his only New Zealand cap in 2020.
"Both are out for the Super (Rugby) campaign, unfortunately," Robertson said.
"Really disappointed for both of them, they're such big contributors to our team and really important parts of it."
