The tribunal was in an unforgiving mood on Wednesday night, also sentencing Fremantle midfielder Jaeger O'Meara to one match on the sidelines for a dangerous tackle.
Zorko and O'Meara will miss their sides' respective post-bye clashes with Hawthorn and Richmond in round 13.
Former Lions captain Zorko pleaded not guilty to "unreasonable or unnecessary contact to the eye region" of Adelaide's Luke Pedlar and was not called to give evidence.
In Zorko's defence, Brisbane lawyer Adrian Anderson admitted the midfielder made "unusual" contact to Pedlar's face but argued there was no direct contact with the Crows forward's eye region.
Anderson also referenced Adelaide's medical report, which noted Pedlar was checked by the club doctor after the incident but "did not recall incident and reported no contact to eye region".
Tribunal chair Renee Enbom said video footage captured Zorko's finger "bent and in a scratching-type position".
"The finger moves down and in our view into the vicinity of the eye socket," Enbom said.
"Accordingly, we are satisfied that contact was made to the eye region.
"Contact was not made to the eye itself, which in our view explains why Pedlar did not react to the incident.
"It also provides an explanation for the comment in the medical report."
The tribunal panel, which included past players Jason Johnson and Scott Stevens, agreed with the match review officer's grading of Zorko's actions as intentional conduct, low impact and high contact.
AFL lawyer Sam Bird said of Zorko's action: "It ought to be seen as an attempt to intimidate a player in a way that, in the current game, has no place."
Zorko's latest suspension adds to a tribunal record that includes seven penalties for striking, four misconduct charges and a fine for staging.
The 34-year-old, 239-game veteran was also fined $2000 for making unnecessary contact with Carlton player Marc Murphy's eye in 2018.
O'Meara was one of 20 players charged with rough conduct over a dangerous tackle across the opening 11 rounds of this season.
The Dockers on-baller attempted to beat his ban by arguing the impact of his tackle on Melbourne's Charlie Spargo, whose head hit the turf in the incident, was "low" rather than "medium".
The tribunal panel disagreed with that submission.
The panel said Spargo's one pinned arm, the rotation in the tackle and a "forceful, driving action" created enough danger to warrant the higher grading.
"Whilst Spargo was not injured in the incident, we consider that there was real potential to cause injury," Enbom said.
Carlton's Adam Cerra and Adelaide's Rory Laird became the first players to overturn bans for dangerous tackles this season when they were successful at the tribunal on Tuesday night.
Sydney co-captain Luke Parker was unsuccessful in his attempt and will serve a one-match suspension.
