Burnett appealed the penalty, which had been set to take effect immediately. He can continue to pitch until a hearing is held.
"You kind of expect something to happen when the ball comes that close," Burnett said before New York played the Rangers in the series finale.
Burnett said it was the first time he'd been suspended. He seemed a bit surprised by the severity, and said his first reaction when told was: "Really?"
Both Burnett and Padilla were fined undisclosed amounts by Major League Baseball.
Cruz had homered earlier, and plate umpire Doug Eddings warned both teams after Burnett's pitch sailed past Cruz.
"That's a fastball in, man, whether it got knocked down or not," Burnett said after the game. "I mean, that's where it's going.
"Warnings are warnings, man. ... You've still got to go about your business and pitch in, don't pitch in."
Said Teixeira after it was over: "I think there was a little message sent."
Padilla said he did not mean to plunk Teixeira.
"The answer is that it's stupid if he thinks it was an intentional pitch," he said through a translator after the loss.
Burnett is 4-2 with a 4.69 ERA in 11 starts.
Padilla is 3-3 with a 5.57 ERA in nine starts. He has hit seven batters, second in the AL to Boston knuckleballer Tim Wakefield.