Michael Matheson has written to Westminster Health Secretary Andrew Lansley to ask whether he would support a move to introduce a ban across the UK.
It follows recent research from Newcastle University which suggests children are still being exposed to the same levels of advertising for such foods, despite Ofcom banning them during programmes aimed at youngsters.
Mr Matheson said: "Broadcast advertising influences the choices made by children and can shape their attitudes to food as they grow into adulthood.
"Tackling obesity and encouraging people to make healthier life choices is one of the most important things we can do to improve the health of our nation.
"The reality is that broadcast advertising is delivered across the UK and we need strong action and co-operation between governments to address this issue.
"According to the UN and Ofcom studies, the restrictions brought in by Ofcom have been adhered to by children's channels and broadcasters showing programmes specifically aimed at children.
"However, a loophole exists that allows HFSS (high in fat, sugar and salt) food adverts to feature during programmes with a high child audience such as soaps and talent shows."
A Department for Culture, Media and Sport spokesman said: "The Government continues to keep this area under review and recognises that there are calls for increased restrictions on HFSS food and drink advertising.
"However, it is widely accepted that advertising has a modest, direct effect on children's food choices and is just one aspect in determining children's choice of food."