Williams was sent off 25 minutes into the Test after a shoulder charge to the head of Lions wing Anthony Watson.
The punishment rules Williams out of the deciding Test next weekend after the Lions levelled the series with a 24-21 victory in Wellington.
Williams, who did not contest the charge, appeared before an all-Australian judicial panel in a near three-hour hearing on Sunday evening at the New Zealand Rugby offices.
Lions flanker Sean O'Brien is also going to appear before the panel after being cited for a swinging arm hit on All Blacks wing Waisake Naholo.
Lions assistant coach Graham Rowntree said Leinster forward O'Brien was "outstanding" in the 24-21 victory at the Westpac Stadium.
"He's the barometer of our energy and aggression in the game," Rowntree said. "His ball pressure, his tackling, his carrying - he's been outstanding.
"We've got a class group of back rowers and I'd have no qualms about anyone else stepping up."
All Blacks coach Steve Hansen confirmed before the hearing that Williams would plead guilty.
"There's a (judicial) process, we trust the process. Sonny's paid a big price. The team's paid a big price for him making a mistake," Hansen said.
Fekitoa replaces Williams
After the hearing on Sunday, Williams said he was "really disappointed, but happy with being able to get in there and say my piece.
"They've come to the conclusion that it was reckless - it wasn't intentional. I'm very disappointed that I've let my brothers down."
The All Blacks have already called Otago Highlanders centre Malakai Fekitoa into the squad as Williams's replacement with senior midfielder Ryan Crotty already sidelined by a hamstring injury sustained in the first Test.
Although the All Blacks were forced to play with 14 men for 55 minutes after Williams was sent from the field, the Lions did not hit the lead until three minutes from full-time when Owen Farrell landed the match-winning penalty.
Williams is the third All Black to receive a red card following Cyril Brownlie in 1925 and Colin Meads in 1967.
The Lions will face the All Blacks in the series decider at Auckland’s Eden Park on Saturday.