Of course girls can be a marketing manager. In IIMs you don't choose your domain right away. You join a post graduate diploma course where in specialization comes to the picture only in the second year. Basically you choose your courses from a variety of electives offered in the second year and based on them you specialize in a particular domain. So,  if you are interested in marketing you can choose marketing electives. Some colleges also let you specialize in the kind of marketing you want to do. For example in marketing you can choose to specialize in FMCG marketing or retail marketing and so on. In other colleges like FMS, XLRI, MDI also it works in almost the same way.

Yes definitely Girls can become Marketing Manager. For pursuing career in Marketing field you will need to do specialization in Marketing Management.

In most of the colleges when you will be joining to start pursuing your MBA degree then in the first year you will be taught subjects from all the different streams in management. Then at the end of second year you will be asked to choose in which stream you want to do major specialization and minor specialization. As you want to become a marketing manager so you will newd to pick Marketing Management as a major and according to your interest you can pick one of the other stream as your minor specialization. Generally HR, Analytics and operations are good stream as a minor with Marketing.

In case of IIMs it will be a little different as there is no major or minor, you get a General Management degree. And at the end of the second year you will be asked to choose all the subjects you wantbto study in second year. For your career you can pick maximum marketing subjects mixing it with some other stream subjects you like.

As a little detail information I would tell you that after doing MBA in most of the companies you won't directly become a marketing manager. Every company has a different hierarchy and mostly it starts with you as a sales manager which is mostly field work and it takes 2-3 years for you to get promoted to as a marketing manager.

All the best!!