League organisers said that Williams was free to resume playing on September 1 after the remaining games this season were taken into account.
Williams received a yellow card following the first-half incident in Belfast last Friday night that resulted in Wales international Patchell being carried off and taken to hospital, where he was detained overnight.
The Ulster forward appeared before an independent PRO12 disciplinary committee on Wednesday.
In a statement, the PRO12 said: "The disciplinary committee, chaired by Roger Morris (Wales), along with Rhian Williams (Wales) and John Doubleday (England), having viewed footage of the incident and listened to representations made by and on behalf of the player, found that the incident was at the top end of the World Rugby sanctions for this type of offence, meriting a 16-week starting point.
"In the absence of any aggravating factors and in light of several mitigating factors, including the player's exemplary previous playing record, the disciplinary committee applied an eight-week reduction from the entry point and suspended the player from playing for eight weeks.
"Taking into account the matches remaining this season, and two warm-up matches scheduled for the start of next season, Nick Williams is free to resume playing from Monday, 1 September 2015, and has the right of appeal."