Any visitor who is not staying the night must pay a 5 euro ($5.35) entry fee online before walking into the lagoon city on April 25 - a national holiday and the first of 29 days this year
The label designs by Taipei-based Aaron Nieh Workshop show the faces of Tsai and her future vice president, Chen Chien-jen, made up from coloured squares reminiscent of eight-bit video games popular in the 1980s.
With only 720,000 bottles released on Monday, customers were quick to fill their shopping baskets.
"I think the packaging is very creative and stylish," shopper Lin Wan-lin, 31, told Reuters.