Shepherd, who made his first Cup start in 1970, is entered for Sunday's race at New Hampshire Motor Speedway in the No. 52 Toyota.
"This is truly a milestone," Shepherd said on his website, "and I thank all who are involved to help make this happen."
His last start in NASCAR's Cup series was in 2006, when he was 64, also at New Hampshire.
Shepherd would break the oldest-driver record held by Jim Fitzgerald, who started a race at age 65 at the now-defunct Riverside (Calif.) International Raceway in 1987.
Born two months before the United States entered World War II, Shepherd in recent years has mainly driven in NASCAR's second-level Nationwide Series.
He's made four Nationwide starts this year and finished 35th or lower each time, typically running fewer than 30 laps. He also failed to qualify for four other Nationwide races.
In the Cup series, Shepherd has 514 career starts and four wins, his last coming at Atlanta in 1993.