Major League Baseball also fined both players an undisclosed amount.
Bard was suspended for "aggressive" actions in the top of the 11th inning of San Diego's 4-2 win over Pittsburgh. Sheffield was ejected for arguing a called strike in the fifth inning of Detroit's 11-5 loss in Cleveland.
Because of the appeals, both players were available Friday night -- Sheffield again against the Indians, and Bard in Washington.
When he was ejected, Sheffield broke his bat and threw a splintered piece to the ground toward Gibson in disgust.
The suspensions will be effective when the appeals process is exhausted.