Updated 6 March 2012
If Dr Su Lian Tan is the first Malaysian (or at least Malaysian-born) to graduate from Juilliard, Dr Nicholas Ong should be the second.
He began piano lessons aged six, and holds a Doctorate in Piano Performance (D.M.A.) at Juilliard, in addition to an M.M from Peabody Conservatory & a Diplome Superieur de Concertiste, Ecole Normale de Musique de Paris, France.

Thanks again to devyerlih.
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Updated 5 March 2012
Looks like there’s someone Malaysian-born who graduated from Juilliard even earlier.

Dr Su Lian Tan (born 1964) [or perhaps better known as Tan Su Lian in this part of the world], was born in Malaysia and was a child prodigy too. The flute being her favourite instrument, she turned pro at 14, and is currently professor of music at Middlebury College in Vermont, USA.
She holds a Ph.D and M.M. from Princeton University, an M.M from the Juilliard School, and a B.A from Bennington College.
Thanks to devyerlih.
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2 March 2012
Juilliard is probably the world’s most prestigious performing arts school. Established in 1905, it’s located at the Lincoln Center for the Performing Arts in New York City.
It trains a few hundred undergrad & graduate students in dance, drama, and music.
Students can borrow top notch musical instruments, including 4 Guarneri and 2 Stradivari violins. The school has 253 Steinway pianos, the largest collection of any institution in the world for the world’s top piano brand.
Juilliard graduates have won many top awards, including 105 Grammy Awards, 24 Academy Awards (Oscars) and 16 Pulitzer Prizes.
It’s notoriously difficult to gain admission into. Typically less than 10% of applicants would be successful.
Malaysian piano prodigy Tengku Ahmad Irfan Tengku Ahmad Shahrizal, 13 auditioned for Juilliard in February 2011, in front of Dr Yoheved Kaplinsky, Juilliard’s pre-college artistic director and professor of music. She has served as judge at the world’s top music competitions, including the Tchaikovsky Competition and the Van Cliburn International Piano Competition.

That should make even the best pianists feel slightly nervous.
Yet, his performance was such that she was impressed – even called him a genius, a rate talent, who has shown “sophistication and depth” in his piano playing and composition.
He has since enrolled in September 2011, pursuing a double major in piano and composition as well as an elective in conducting, and has progressed to such an extent that “his compositions are so mature and sophisticated that even his teachers are amazed.”
Tengku Ahmad Irfan performing the 3rd movement of Chopin Piano Concerto No.1 during Konsert Permata Seni 2010. At that time he was only 11 years old
Source
The Star, 3 Mar 2012
New Straits Times, 3 Mar 2012