The incident happened during Sunday's 2-2 draw between the sides.
The 26-year-old later apologised for biting the Chelsea defender and was fined by Liverpool on Monday.
The club, who have until Friday at 12:00 BST to appeal, said they were "shocked and disappointed" at the length of the suspension.
Uruguay international Suarez had accepted the FA charge of violent conduct but claimed his ban should be three games, the standard punishment for violent conduct.
An FA statement read: "A three-person Independent Regulatory Commission today upheld The FA's claim that a suspension of three matches was clearly insufficient and the player will serve a further seven first-team matches in addition to the standard three. The suspension begins with immediate effect.
"The Liverpool forward had accepted a charge of violent conduct but had denied The FA's claim that the standard three-match sanction was insufficient for the offence.
"The incident was not seen by the match officials and has therefore been retrospectively reviewed.
"Suarez has until midday on Friday, 26 April to appeal the additional suspension, above the standard three matches."
The ban covers their final four games of this season, and the first six games of 2013-14.
LFC managing director Ian Ayre said: "Both the club and player are shocked and disappointed at the severity of today's Independent Regulatory Commission decision.
"We await the written reasons tomorrow before making any further comment."
It is not the first time Suarez has been charged with such an offence. He was banned for seven games when he was at Ajax after biting PSV Eindhoven midfielder Otman Bakkal's shoulder during a match in November 2010.
During his time at Liverpool, he was also given an eight-match ban and £40,000 fine by the FA for racially abusing Manchester United left-back Patrice Evra in December 2011.
-BBC
