If you mean classic CPG marketing, I don't think any of the ones that came to Stern hire internationals full-time. I could be mistaken. However, pharmaceutical companies (Pfizer, BMS etc) hire international students into marketing at non-US locations. Others like American Express and companies, especially in travel and hospitality, will hire and sponsor international students for *some* positions.
So your options are limited if you are not a US resident and interested in marketing, but they're not non-existent either.
Internships however aren't a problem. But you need to be aware that spending a summer in marketing at Kraft, Colgate, L'Oreal, Hermes, or Unilever etc. may not necessarily lead to a full-time offer if you're international.
gijoedude
But can you please answer a question of mine? How open are these companies to internationals? I know banks and consulting companies easily sponsor H1B if needed, but what about these marketing companies? Do they prefer citizens/PR?