"Our ambitions are higher than having seasonal tourism. Tourism is key driver of our economy and we aim to make the UAE an attractive destination all year long," said Sheikh Mohammed.
"This is why we will start working on providing pleasant temperature-controlled environments during the summer months."
The statement issued late on Saturday did not say when construction would begin, nor did it reveal the cost of the project.
Dubai hopes the "Mall of the World" can attract more than 180 million visitors each year.
The emirate is known for its numerous malls and many hotels, including the Dubai Mall, touted as the world's largest shopping, leisure and entertainment destination. It is also home to the world's tallest tower, Burj Khalifa.
Dubai has established itself as a global hub for air transport and transit trade, as well as a regional financial centre.