The first single, "On traverse un miroir" entered the Quebec Airplay Chart on 25 April 1987 and peaked at number two. The second single, "Incognito" debuted on this chart on 6 June 1987 and topped it for six weeks. The next single, "Lolita (trop jeune pour aimer)" entered the Quebec Airplay Chart on 3 October 1987 and occupied the number-one position for two weeks. The fourth single, "Comme un cœur froid" debuted on the chart on 6 February 1988 and also topped it for two weeks. The fifth single, "Délivre-moi" entered the Quebec Airplay Chart on 18 June 1988 and peaked at number four. The last Canadian single, "D'abord, c'est quoi l'amour" debuted on the chart in Quebec on 17 October 1988 and became Dion's fourth number one from Incognito spending two weeks at the top. "Jours de fièvre" was released as a single in Denmark in late 1988.
On 23 November 1987, Incognito was certified Gold by the CRIA for selling 50,000 copies. On 16 September 1988, it was certified Platinum in Canada for selling 100,000 units. Later, on 31 January 1996 the album was certified two-times Platinum by the CRIA for sales of over 200,000 copies. In Belgium Wallonia, Incognito entered the Ultratop 200 Albums chart in 1995, thanks to the success of D'eux and peaked at number sixty-five on 11 November 1995. Incognito has sold over 500,000 copies worldwide.
In 1987, Dion was nominated for the Félix Award for Female Vocalist of the Year and Incognito was nominated in category Pop Album of the Year. Jean-Alain Roussel won Félix Award for arranging "Comme un cœur froid" and was nominated for two other Félix Awards for producing and engineering "Incognito." In 1988, Dion won Félix Award for Female Vocalist of the Year and "Incognito" won in category Most Popular Song of the Year. Thanks to the Incognito tournée, Dion also won Félix Award for Best Stage Performance of the Year and was nominated in category Show of the Year. Incognito tournée also won Félix Award for Stage Director of the Year and was nominated in category Stage Designer of the Year and Lighting Designer of the Year. Dion was also nominated for the Juno Award for Most Promising Female Vocalist of the Year in 1987 and Female Vocalist of the Year in 1989. She was also nominated for three MetroStar Awards in 1987 (Female Vocalist of the Year, Young Artist of the Year, Female Personality of the Year) and four in 1988 (Female Vocalist of the Year, Young Artist of the Year, Female Personality of the Year, Jury Award), and won MetroStar Award for Young Artist of the Year in 1988. Dion's television special titled Spécial Incognito was nominated for six Gémeaux Awards in 1988 and won two for Best Cinematography and Best Lighting. Other nominations included Best Direction, Best Production Design, Best Costume Design and Best Makeup/Hair.