The suspension was announced by Joe Garagiola Jr., the MLB senior vice president of standards and on-field operations.
Smith confirmed Thursday that he put the substance on his forearm before warming up in the bullpen on a brisk night. He said he regretted not wiping it off before entering the game.
"It was chilly and kind of windy," Smith said. "I had rosin and sunscreen on my arm. I just forgot to wipe it off before I went out and pitched. I had to kind of get ready in a hurry. I just forgot. That's it."
It's widely acknowledged pitchers use similar practices to grip the ball better even though it's against the rules.
With the bases loaded and one out and Atlanta leading 2-1, Braves manager Fredi Gonzalez emerged from the dugout and asked the umpires to check whether Smith had pine tar on his arm.
"It was about as plain as it could be," Gonzalez said. "It's pretty blatant, really. It's glistening through the lights. You could see it in the dugout."
After all four umpires gathered around Gonzalez, crew chief Jim Joyce walked to the mound, touched Smith's arm and tossed the reliever from the game.
The Associated Press contributed to this report.