The accident happened yesterday at the Jim Clark rally near Kelso, close to the English border.
Five people suffered minor injuries when a car collided with spectators in an earlier accident during the same rally, police said.
"Investigations into both incidents are ongoing," Police Scotland said in a statement.
The rally is named after Scottish Formula One driver Jim Clark, who was killed in a motor racing accident in Germany in 1968.
It takes place over three days on closed roads.