The milkshakes, available in chocolate and strawberry are sold in Asda, Waitrose and Morrisons stores nationwide.
The Happy Monkey Milkshakes are packed in the Tetra Pak Prisma Aseptic 200ml carton with a straw.
Happy Monkey managing director Greg Boyle said: "We are really excited about the launch of our revamped Happy Monkey Milkshake range, and we think that the colourful, easy-to-hold cartons will appeal to parents looking for a fun, convenient and nutritious drink for their children.
"The fact that the cartons are made from renewable materials and are still easy to recycle was also a key factor in our decision to make the move."
Tetra Pak UK & Ireland portfolio manager Mike Jarvis said: "We have seen huge growth in the flavoured milk category recently, and it is now the second most widely consumed liquid dairy product after white milk worldwide. With this in mind, it's a really exciting time to be working with such a fun and family-oriented flavoured milk brand.
"Our distinctively shaped Tetra Prisma Aseptic carton is perfect for Happy Monkey, and will help give the range the stand-out, on shelf appeal it deserves.
"Like Happy Monkey Milkshakes, this pack format is also ideal for the modern family, with a convenient shape and size, perfectly suited for growing kids and busy mums."