For Roddick, whose world ranking has slipped to 27th, it was his earliest exit from the Memphis tournament in 12 appearances. Malisse, ranked 75th, was winless in four matches this season and in nine career matches against Roddick.
Roddick, seeded No. 2, has been slowed by hamstring and ankle problems this season. He was unable to capitalize on two set points in the first and was broken in the 12th game of the second by the 31-year-old Malisse.
No. 4 seed Milos Raonic, champion of last week's ATP World Tour event in San Jose, plays in a late match Wednesday.
In other men's first-round matches, No. 3 seed Radek Stepanek won 6-3, 6-2 over qualifier Bobby Reynolds, No. 7 seed Kevin Anderson advanced with a 7-5, 6-3 victory over qualifier Robby Ginepri and Jurgen Melzer of Austria beat Denis Istomin of Uzbekistan, 6-7(2), 6-3, 7-6(4). Istomin was coming off a runner-up finish in San Jose.
In the Memphis International, the accompanying Women's Tennis Association event, Alberta Brianti of Italy eliminated No. 2 seed Ksenia Pervak, 7-6(3), 6-2, while Sofia Arvidsson, the 2006 champion, joined Brianti in the quarterfinals with a 7-6(5), 0-6, 6-3 upset of No. 5 seed Pauline Parmentier.
Only one of the eight women's seeds -- No. 4 Marina Erakovic -- remains moving into Thursday's quarterfinals.