The suspension means the 34-year-old will be unavailable for his club's opening Pool 2 games against Newport Gwent Dragons and Biarritz, as well as December's double header with Glasgow.
Azam originally insisted any contact with Borthwick had been accidental but he since pleaded guilty at an RFU disciplinary hearing in Bristol.
The former Clermont Auvergne front rower will also miss six Guinness Premiership fixtures and will not be eligible for selection until December 29.
Borthwick required five stitches in an eye wound after the incident at Vicarage Road and it was feared that he would face a lengthy lay off if damage had been done to his eye socket.
Fortunately for Saracens and for Borthwick, further medical tests showed that he was instead suffering from extreme swelling and tissue damage.
The Sarries skipper is expected to return to action in time for his club's Amlin Challenge Cup tie away to Toulon on October 15.