Tavarez was suspended for five games, and Davis was suspended for three games, and both were fined undisclosed amounts, said Frank Robinson, vice-president of on-field operations for major league baseball.
Tavarez and Davis will decide Friday whether to appeal.
The suspensions were the first issued during spring training since T.J. Mathews, then with St. Louis, admitted he threw at Bret Boone, then with Cincinnati, in March 1997. Mathews was suspended for six games, lost his appeal and served the penalty in the regular season.
If they do not appeal, Tavarez and Davis will begin their suspensions on April 2. The Cubs are home against Montreal that day while the Giants are home against San Diego.
Last Monday, Tavarez dropped to one knee after striking out Davis in Mesa, Ariz. Davis saw it as a sign of celebration and exchanged words with Tavarez.
Davis then charged the mound and Tavarez took a flying kick at the Giants infielder. The players punched at each other, triggering a bench-clearing brawl, and Tavarez and Davis were ejected.
