In a message to His Majesty The King of Malaysia she said: "I have much pleasure in sending you and the people of Malaysia my very best wishes on the occasion of your 50th anniversary of Independence."
She added that she was delighted that her son, The Duke of York, has travelled to the country to represent her.
Prime Minister Gordon Brown sent his own message to Malaysian Prime Minister Abdullah Badawi speaking of the country as "an inspiration".
He said: "At a time when the world still faces tremendous challenges on global development, Malaysia stands out as an inspiration.
"In 50 years, Malaysia has made huge strides towards reaching the goal of developed nation status by 2020, and shows the way for other developing countries. The UK is proud to have been a partner of Malaysia during this success. Our relationship is rich both in breadth and depth."
Earlier, Andrew looked on as veteran British servicemen who fought to defend Malaysia more than 45 years ago took part in a spectacular display.
The old soldiers marched through the streets of Kuala Lumpur in a national day parade celebrating the Far East nation's people, history and achievements as heads of governments and thousands of spectators looked on.
The veterans wore for the first time a campaign medal awarded by the Malaysian government as they strode through Merdeka Square in brilliant sunshine - the site where independence was declared on August 31 1957.
Non-British awards are not normally allowed to be displayed but the former servicemen were given permission by the Queen to wear the Pingat Jasa Malaysia medal - but only for a three-week period that covers the country's independence celebrations.