The back-rower pleaded guilty to a charge of striking after appearing to elbow New Zealand lock Brodie Retallick in the face during his side's 37-10 defeat to the All Blacks at Eden Park on Saturday.
The incident was missed by the match officials, but Mumm was cited and has subsequently pleaded guilty.
The 32-year-old has been handed a one-week ban rather than the usual entry ban of two weeks due to mitigating factors, but will still miss the November 5 trip to the Principality Stadium.
"Taking into account mitigating factors including the player's early plea and his excellent disciplinary record, I reduced the suspension to a period of one week," SANZAR judicial officer Robert Stelzner said in a statement.
Retallick later left the field with concussion and is a doubt for New Zealand's tour.