It was determined Tepera, 33, had intent when he threw behind and at the feet of Woodruff in the fifth inning. By rule, manager David Ross received a one-game suspension, which he'll serve Friday.
Tepera is appealing the punishment, which will be held in abeyance until the process is complete.
MLB also handed out a one-game suspension to Cubs associate pitching, catching and strategy coach Mike Borzello, according to a source.
Tempers have been running high between the teams. Cubs catcher Willson Contreras has been hit by a pitch three times in April by the Brewers, including once in the head. Contreras was fined $7,500 for inciting the benches to clear in a series at Wrigley Field.
On Tuesday, Contreras was hit again, leading to Tepera nearly hitting Woodruff one inning later. Contreras hit a go-ahead, two-run homer off Brent Suter after he was hit by the pitch, helping the Cubs win 3-2.
Bench coach Andy Greene will manage the Cubs on Friday when they open a series against the Atlanta Braves. The Cubs and Brewers play their third series of the season later this month.