Dodoni Ice Cream was founded in 1987 and became a franchisor in 1991. The company currently has 75 outlets and distribution deals with a further 300 stores.
A Vivartia spokesperson described the move as an investment decision. Vivartia sold its own ice cream unit to Nestlé two years ago.
Under Greek corporate law, once a company has acquired more than 33% in another it is required to make a formal takeover offer within 20 working days. Marfin passed this mark on 16 July and is expected to table a public offer by 13 August.
Vivartia is the market leader in a number of food categories in Greece and has operations in 29 countries.