Williams re-injured the troublesome knee, which he also had surgery on last year, late in the Blues victory over South African side the Stormers last month.
The 33-year-old then missed their fourth straight win, against the Waratahs last weekend, before the Blues on Thursday confirmed he would undergo minor arthroscopic surgery on Friday.
Blues coach Leon MacDonald said Williams' injury was a big blow for him and the team.
"I feel sorry for him. It's unfortunate, he's obviously landed on it awkwardly and has caused some damage there. For him to have a return-to-rugby plan will help. We'll miss him on the rugby field, obviously, but he's still contributing in the meeting rooms and where he can."
"Whatever he puts his mind to, he makes happen. If he still wants to play later on he's the sort of guy you'd never write off. This year he really wants to make the World Cup squad and be a part of that obviously, so he's driven to recover well from this injury and get back on the field," MacDonald said.
The procedure also means he will miss the first of this year's foundation days for the wider All Blacks squad, which is being held in Wellington on Monday.
Williams won't be replaced for the All Blacks foundation day, in which 41 players were named on Tuesday.
An absence of six weeks would mean the 51-test midfielder would be back for the Blues derby clash with Crusaders in Christchurch on May 25.
That would give Williams four Super Rugby matches, plus potential playoff games, to further push his case for inclusion in the first All Blacks squad of the year.