Grubb was suspended for actions "detrimental to stock car racing."
He will be required to attend counseling sessions and meet other conditions for reinstatement, including random drug testing, NASCAR said.
"NASCAR has zero tolerance for any type of behavior that is in violation of our substance abuse policy. We have a moral responsibility to protect the integrity of our sport," said Mike Helton, NASCAR president.
Grubb raced 25 times last season and finished 19th in the Busch Series standings. He had not raced yet this season.
Shane Hmiel, another Busch driver, was suspended Sept. 18, 2003, for violating the substance abuse policy and was reinstated last month.