Suarez accepted a charge of violent conduct after the incident in the 2-2 Premier League draw at Anfield on Sunday but disputed the FA view that it merited more than a three-game ban.
An Independent Regulatory Commission met in London on Wednesday to decide the Uruguayan international's fate and added seven games to the usual ban for violent conduct.
The suspension begins immediately, meaning Liverpool's leading scorer will miss his side's last four games of the season and the first six at the beginning of next term.
Liverpool, who expressed their shock at the Commission's decision, have until Friday to appeal.
"Both the club and player are shocked and disappointed at the severity of today's Independent Regulatory Commission decision," Liverpool managing director Ian Ayre said in a statement.
"We await the written reasons tomorrow (Thursday) before making any further comment."
Suarez's bite on Ivanovic's arm at Anfield was missed by referee Kevin Friend but television replays showed him sinking his teeth into the Serbian.
The 26-year-old Suarez, who was banned for biting an opponent while with Dutch club Ajax before joining Liverpool in 2011, apologised after the game and was fined a reported £200,000 by the club.
However, he was widely condemned for his behaviour with some reports suggesting he was in danger of being sacked by the club, although Liverpool said this week that they wanted the Uruguayan to see out his four-year contract.
The FA said a three-match ban was "clearly insufficient" for the serious nature of the offence.
There was widespread support for the length of the punishment imposed with former Liverpool player Graeme Souness telling Sky Sports News: "I think 10 games is about right.
"What he did on Sunday is something I've never seen in a game anywhere before."
Former Liverpool midfielder Jamie Redknapp agreed.
"I think you have to accept that the crime that he committed probably warranted a 10-game ban," he said.
"It was an awful act of brutality really what he did and now he won't play for such a long time - it's is going to hit him where it hurts because he wants to play football."
Professional Footballers' Association chief executive Gordon Taylor said the length of the sanction sent out a "strong message" but that it was important that the player received counselling to make sure it did not happen again.
Not everyone backed the FA's decision.
"Players who break peoples' legs, who do horrible tackles, get a three-game ban," former Liverpool striker John Aldridge told Sky Sports News.
"It's inconsistent. For me, it's not right, it's over the top."
Controversy has followed Suarez since he joined Liverpool, with his antics often overshadowing his impact on the pitch.
He served an eight-match ban for racially abusing Manchester United's Patrice Evra last season and later angered United manager Alex Ferguson by failing to shake the French defender's hand before their league match in February last year.
He has also been regularly accused of diving to win penalties and free kicks, while in an FA Cup tie this season against minor league Mansfield Town he was again criticised for scoring a goal despite a blatant handball.
Until Manchester United forward Robin Van Persie's hat-trick against Aston Villa on Monday that secured the title, Suarez was leading scorer in the league with 23 goals and he is included on a six-player shortlist for PFA Player of the Year.
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