The two portraits form part of the auction house's Impressionist and Modern Art sale on February 2.
The Picasso, Tête de femme, is a portrait of the artist's second wife, Jacqueline, painted in 1963, two years after they had married.
It has been unseen in public since 1967 and in the same collection since 1981.
The subject of many of his paintings, Jacqueline had a very short neck and the artist would exaggerate its length for comic effect in his portraits. Christie's expects the painting to sell for between £3 million and £4 million.
The Renoir, Mademoiselle Grimpel au ruban rouge, shows Hélène Grimpel, the granddaughter of Armand Grimpel, a wealthy banker who became a great patron of the artist.
The painting, expected to fetch between £1.8 million and £2.5 million, has been in the same French collection for 60 years and has not been exhibited since the 1960s.