Suu Kyi was first held under house arrest 19 years ago, and has spent almost 13 years as a captive ever since. Currently, she stands accused of breaking the terms of her confinement.
Hollywood stars like Julia Roberts and Demi Moore have posted their messages on the website 64forsuu.org as a part of the campaign marking Suu Kyi's 64th birthday on June 19.
"We must not stand by as she is silenced again. Now is the time for the international community to speak with one voice," the Telegraph quoted Roberts as having written on the website.
Kevin Spacey, Yoko Ono, Gordon Brown, Stephen Fry and Eddie Izzard have also joined the campaign.
The supporters of the Burmese have been invited to tweet, write text messages or send video and photos supporting Suu Kyi.