The 40-year-old Grundy turned himself in Friday and appeared in court Saturday.
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A police report said Grundy told police he knew he hit something on Dixie Highway in Louisville on the night of June 7, but did not stop.
Police said a woman trying to cross the road died after being struck.
Grundy also faces charges for having no driver's license, no auto insurance and expired tags.
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Grundy has had numerous DWI arrests in North Carolina in the past, including in Wake County and Nash County.
Grundy played guard for the Wolfpack from 1998-2002 and was First-Team All ACC during his senior season.
He played briefly in the NBA but had a long career playing basketball overseas.