Suarez sunk his teeth into Serbian defender Branislav Ivanovic as they tussled for the ball in the penalty area with Liverpool trailing 2-1 in the Premier League game.
Referee Kevin Friend appeared not to see the 66th-minute incident but Suarez - who once served a seven-match ban for biting an opponent in the Netherlands while with Ajax - faces a suspension once his moment of madness is reviewed.
"I am deeply sorry for my inexcusable behaviour earlier today during our match against Chelsea," Suarez said.
"I have issued an apology and have tried to contact Branislav Ivanovic to speak to him personally. I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down."
Chelsea's interim boss Rafa Benitez was reluctant to talk about it, but Suarez's action was slammed by pundits, including former Liverpool captain Graeme Souness.
"I'm not sure what to make of it," Souness told Sky Sports. "Embarrassing. He's making it very difficult for himself to stay at Liverpool, that puts him in the last-chance saloon.
"Most important is safeguarding the good name of the football club. Liverpool are world renowned. People will be talking about this for a long, long time, and it will show Liverpool in a very bad light.
"This is not the first time he has bitten someone in the football match.
"There are lines you just can't cross, and he has crossed it today. Those pictures will be beamed across the world. It's very difficult for Brendan Rodgers to defend him."
Fellow pundit Jamie Redknapp, another former Liverpool player, added: "He obviously has a big problem. He has that madness gene in him, and what he did today was indefensible.
"What is he doing? Why would you want to take a chunk out of someone's arm on a football field?"
Suarez served an eight-match ban for racially abusing Manchester United's Patrice Evra last season and later angered United manager Sir Alex Ferguson by failing to shake the French defender's hand before their league match in February last year.
