Asda was found in breach of code 3.2, which governs the naming, packaging and promotion of alcoholic drinks.
The Portman Group investigated the pack after receiving a complaint from a member of the public saying that the product was "designed to attract children".
David Poley, chief executive of The Portman Group, said: "These companies have overstepped the mark with this irresponsible marketing. The Portman Group has repeatedly warned the industry about the risks of selling alcohol with cuddly toys. In future, we hope that all alcohol gift pack producers will seek pre-sale advice on responsible marketing from The Portman Group."
Last June, the Portman Group ruled that the Bubbly and Bear gift pack available in Asda stores also breached its code by appealing to under-18s.