Rigg and her actress daughter Rachael Stirling will both appear in a 2013 episode of the BBC drama, written by Mark Gatiss.
Of the Avengers star, Smith told TV Guide: "She's totally wonderful and has some amazing lines."
He added: "You just sort of melt when she says [them] 'cos she's brilliant. She's going to be great."
Doctor Who returned to BBC One for its seventh series on Saturday night, pulling in an overnight audience of 6.4m viewers.
The series continues this Saturday (September 8) on BBC One and BBC America with 'Dinosaurs on a Spaceship'.