The incident occurred during a 3-2 win over the Brewers on Tuesday in Milwaukee. MLB announced the disciplinary measures Thursday.
Tepera received a three-game suspension. Ross received a one-game suspension. The amount of their fines was not disclosed.
The Brewers led 2-1 in the bottom of the fifth inning Tuesday when Tepera faced Brewers pitcher Brandon Woodruff. Tepera's first pitch to Woodruff was a 95-mph fastball, which went just behind Woodruff, who jumped out of the way to avoid the offering.
Woodruff and Tepera exchanged words after the incident. The Brewers pitcher hit Cubs catcher Willson Contreras with a pitch earlier in the game.
Contreras admitted after Tuesday's game that the Cubs were trying to hit Woodruff with the pitch. The Cubs posted a montage of Brewers pitchers hitting their batters Tuesday night on Twitter.
"That probably was a mistake by us, trying to hit the pitcher," Contreras said in a postgame interview. "I don't think he's the right guy to do it. I think if you wanna hit somebody, it will have to be a position player."
Ross serves his suspension Friday, while Tepera appealed his suspension and can play until MLB rules on the appeal.
Brewers pitchers have hit Contreras three times so far in April. The Cubs and Brewers reunite for a three-game series from April 23 to 25 in Chicago.