"I'm sad for what happened this afternoon, I apologize Ivanovic and all football world for my inexcusable behaviour. I'm so sorry about it!!," Uruguayan Suarez, who later scored in the 97th minute to grab a 2-2 draw for Liverpool, said on Twitter.
He apologised after manager Brendan Rodgers said the incident would be investigated and no player was indispensible or bigger than the club.
Suarez scored a 97th-minute equaliser to rescue a 2-2 home draw with Chelsea on Sunday in a Premier League match marked by another bizarre incident involving the hosts' controversial striker.
But the post-match headlines are likely to be dominated by the Uruguayan striker for all the wrong reasons as he bit Chelsea defender Branislav Ivanovic after the pair had tussled in the area in the second half.
Liverpool were sparked into life by the introduction of Sturridge at halftime and the former Chelsea striker drew them level with a tap in at the far post on 52 minutes.
Parity was short-lived, however, as Hazard coolly dispatched a penalty five minutes later after Suarez had handled in the area, to put a smile on the face of Chelsea interim manager Rafael Benitez on his return to his former club.
Yet with the six minutes of stoppage time signalled already played, Sturridge crossed for Suarez to glance in a header at the near post that Chelsea keeper Petr Cech could only push into the roof of the net.