The commissioner's office announced the drug penalty on Wednesday. The ban will take effect at the start of next season.
Grandal made his big league debut this year. He hit .297 with eight home runs and 36 RBIs in 60 games. He turns 24 on Thursday.
"I apologize to the fans, my teammates and to the San Diego Padres," he said in a statement. "I was disappointed to learn of my positive test and under the joint drug program. I am responsible for what I put into my body. I must accept responsibility for my actions and serve my suspension."
Grandal was acquired by the Padres from Cincinnati last December. The Cuban native was traded by the Reds with pitcher Edinson Volquez in a package for pitcher Mat Latos.
There have been seven suspensions this year under the major league program. Six of them were for peformance-enhancing drugs—including Melky Cabrera and Bartolo Colon for positive testosterone tests—and one for a stimulant.
The seven suspensions are the most in a year under the big league drug program since there were eight in 2007.
There have been 101 suspensions this year under the minor league drug problem.