Roddick, whose only defeat since August had come in the Davis Cup against Slovakia last month, was blitzed by the big-hitting Massu, who grew in stature as the match wore on.
Defeat for Roddick put a dent in his hopes of replacing Juan Carlos Ferrero as world number one before the end of the year.
Ferrero, who leads Roddick in the ATP entry list by a handful of points, came through a tight match against fellow Spaniard Felix Mantilla 7-6 7-6 to move through to the quarter-finals.
Switzerland's Roger Federer, seeded third and also in with a chance of finishing the year as number one, had a more straightforward 6-3 7-6 victory over American Mardy Fish.
Seventh seed Paradorn Srichaphan of Thailand had a smart win over another American, Jan-Michael Gambill, 7-5 6-4 to set up a quarter-final against Ferrero.
There were several surprises in the third round of the 2.45-million-euro ($2.85 million) indoor tournament, with Feliciano Lopez beating fifth seed Carlos Moya 6-7 6-1 7-5 and Juan Ignacio Chela edging out eighth seed Jiri Novak of the Czech Republic 3-6 7-6 6-2.
The biggest shock of the day was undoubtedly Roddick's straight-sets defeat against Massu.
The Chilean started slowly against the number two seed but, after losing his serve in game six,
Roddick looked punch-drunk as he slipped 3-0 behind in the second set and the American never recovered.
"He played a great match," Roddick said. "I didn't serve well today but otherwise I was okay. I was very impressed with him."
IMPRESSIVE FEDERER
Federer maintained the pressure on the top two with his impressive victory over Fish.
"He was a dangerous opponent," Federer said. "He put me on the back foot and I had to watch out."
The other main point of interest in Madrid is the battle for the two remaining places in the Tennis Masters Cup in Houston at the end of the season.
Frenchman Sebastien Grosjean, in 11th place in the ATP Champions Race, and Paradorn, in 13th, both improved their chances of reaching Houston with straightforward wins against American opposition on Thursday.
Grosjean, the number six seed, beat Vincent Spadea 6-3 6-2.
Moya, seventh in the Champions Race, missed a good chance to close in on Houston with his untidy defeat by Lopez.
Fifth seed Younes El Aynaoui of Morocco completed a nightmare day for the American challengers, making it five defeats in five matches with a 6-4 7-6 success against Robby Ginepri on court number one.