Tepera began his suspension with Sunday's series finale against the Brewers. The Cubs began a four-game series at Atlanta on Monday night.
Tepera also was fined by MLB senior vice president for on-field operations Michael Hill. He appealed the discipline to MLB special adviser John McHale Jr.
The 33-year-old Tepera threw a pitch behind Woodruff in the fifth inning of Chicago's 3-2 victory at Milwaukee on April 13. Cubs catcher Willson Contreras had been plunked earlier in the game, and Tepera said he wanted to send a message because he felt his team had been hit too often in the past couple of years.
The right-hander has a 5.19 ERA in nine relief appearances for the Cubs this season.
Information from The Associated Press was used in this report.