The incident happened during the second half of Liverpool's 2-2 draw with Chelsea at Anfield last Sunday.
Suarez had until 12pm on Friday to appeal, but the FA has confirmed that the club and player have decided against that course of action.
A statement on the FA website said: "Liverpool forward Luis Suarez has not appealed the suspension issued to him by an Independent Regulatory Commission this week.
"A three-person Independent Regulatory Commission upheld the FA's claim that a suspension of three matches was clearly insufficient and the player will now serve a further seven first-team matches in addition to the standard three.
"The suspension begins with immediate effect and applies to Liverpool FC's next 10 domestic first-team fixtures."
The FA confirmed that they would release the Independent Regulatory Commission's written reasons for the ban "in due course".
The ban starts with Saturday's away clash at Newcastle United.