Club managing director Ian Ayre said: "Both player and club are shocked and disappointed by the severity. We await the written reasons tomorrow before making any further comment."
Suarez has until midday Friday to appeal the additional suspension above the standard three matches. With four EPL matches remaining on the calendar, Suarez is ruled out for the rest of the season.
The sanction was imposed Wednesday by an independent regulatory commission on a charge of violent conduct against the Liverpool striker.
An FA statement said: "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."
Suarez bit Ivanovic on the upper right arm during the 2-2 draw at Anfield on Sunday. He wasn't sent off because the referee didn't see it.
It's not Suarez's first offense for biting an opponent. In November 2010, he was banned for seven matches for biting a PSV Eindhoven player in the Dutch league, earning the nickname "Cannibal of Ajax."
On that occasion, the 26-year-old sank his teeth into Otman Bakkal, and although that incident did not form any part of the FA's case as it was in a different country, the commission had the discretion to take his personal disciplinary history into consideration.
There is no standard minimum or maximum punishment for biting in football's disciplinary code, unlike rugby union, which has a 12-week recommended suspension for first offenses up to a four-year ban for the most serious biting offenses.
Suarez also was suspended for eight games in December 2011 for making racist insults toward Manchester United defender Patrice Evra during a match.
The FA has come down hard on Suarez, giving him a more severe ban than it handed to him and Chelsea captain John Terry (four matches) for racist abuse last season. It has parallels with a recent judgment in rugby league, when England international James Graham was banned for 12 games for biting an opponent during an Australian league game.
It's not as heavy, though, as the 12-game ban handed to Joey Barton after he clashed with Manchester City players after his sending-off for Queens Park Rangers on the final day of last season. In 1998, Paolo Di Canio -- the current Sunderland manager -- was suspended for 11 games for pushing a referee while playing for Sheffield Wednesday while David Prutton was banned for 10 matches in 2005 for shoving a referee after being sent off.
With his goals and performances this season, Suarez was starting to rehabilitate a reputation that was first damaged when he was sent off for a deliberate handball to prevent Ghana from scoring a late goal in a World Cup quarterfinal match in 2010. He was seen celebrating on the sideline when Ghana missed the spot kick and Uruguay advanced in a shootout.
His penchant for diving aside, even his critics had been starting to warm to one of the world's most gifted players. He is on the six-man shortlist for English football's Player of the Year award, compiled before Sunday's incident.
Information from The Associated Press and Press Association was used in this report.