Richard Barrington, sent off for his part in the incident, was cleared of dangerous charging by a Rugby Football Union disciplinary panel.
Prop Barrington, 27, is now free to play again immediately, while Barritt, 30, is suspended until 31 January.
An RFU statement said Barritt's ban was in line with new high-tackle laws.
Centre Barritt had initially tackled Parling high and Barrington followed up with a shoulder into the head of the 33-year-old England international, who was carried off on a stretcher.
Under the new interpretation of the high-tackle rules, which came into effect on 3 January, Barrington was sent off by referee Ian Tempest.
However, the panel at Tuesday's hearing in London judged Parling was already unconscious from Barritt's tackle and fell into the contact with Barrington.
"The incident arose out of the specific dynamic of Mr Parling falling unconscious into what would have otherwise been a legitimate contact by Mr Barrington," the RFU statement added.
"In line with the new sanctions a mid-range entry of six weeks was imposed on Mr Barritt reduced to three weeks in light of mitigation including his guilty plea."
Barritt will now miss Saracens' Champions Cup games at Scarlets on Sunday and at home to Toulon on 21 January.
He is also banned for the Anglo-Welsh Cup visit to Scarlets on 27 January, although Sarries tend to rest a number of first-team players in the competition.
Saracens captain Brad Barritt has been banned for three weeks after admitting to a dangerous tackle on Exeter lock Geoff Parling on Saturday.