It completely depends on what kind of internship you would be going into. There isn't really such a thing as a history internship, although you may be able to find internships in other fields that are related to history such as museums or archives. Normally, there aren't any restrictions on working alongside Masters degrees (other than places like Oxford and Cambridge), a lot of people do need to work alongside Masters degrees as unfortunately the student loan does not cover both tuition fees and living costs. The limit, however, would be whether you could reasonably manage the workload of both a internship and a Masters degree. Some Masters degrees might give you the opportunity to do a placement as part of your course, and this and the work you produce off the back of your placement would contribute towards your final mark. Voluntary internships, whilst unfortunately being unpaid, may be a good option as they allow an increasing amount of flexibility. During my Masters degree, I volunteered at a museum and was then taken on as paid staff whilst in the final writing up stages of my dissertation.
Edit: additionally, universities often offer you the chance to work as a research assistant for the lecturers in the department, normally undertaking a specific task within their current research project. I've noticed that these seem to be aimed at undergraduate students moreso than masters students, however, most likely because undergraduate students can do this in their summer holidays but masters students don't normally get a summer break.