I've tutored kids from both
BIS and MIS (Munich International School). There both excellent, if you can afford it. Both are between Euro 10,000 - 15,000 per year, depending on grade level, plus substantial additional enrollment fees.
Both follow the curriculum of the International Baccalaureate Organisation based in Geneva. It is well recognized as an excellent curriculum.
Honestly, I didn't find a lot of difference between the schools. Both have beautiful campuses, first-rate teachers and relatively small class sizes. I guess the choice between the two would depend on if you lived more north (BIS) or south (MIS), although both have extensive bus services for all of Munich.
However, at 4 years old, your little one might be just fine in a German
kindergarten for a few hours a day. Then he/she would be exposed to the language and will almost certainly pick it up fast. Kindergarten here is for ages 3, 4, 5. You could also consider a bi-lingual kindergarten to ease your child into German exposure. See this thread for more information:
Choosing a schooling plan for your children.
Good luck!