Find Birth Record in Tokyo

My grandma was born in Tokyo. Her mom was Japanese and her dad was not Japanese. I did not know which municipal city she was born. How do I find out her birth certificate or her birth record ?

You can't.
The authorities will never provide you information about anyone without your proving you are the family of the person. If they believe someone showing up saying "I'm a grandchild of this person. Can I get all the Koseki information of hers?," personal information can't be protected.

Hire a private detective. The only way that comes to my mind is this.

If you were aware of the individual's name and could prove your identity and your relation to the person, it may be possible to find their Koseki Tohon via hiring an attorney lawyer. Keep inind that as your grandmother's father was not Japanese, the family register is filed under the Japanese person as head of the household.
Also, if you are aware of your great-grandmother's birthplace, it very well may be that your grandmother's documents are also filed there, as Koseki-Tohon are usually filed at the 'ancestral' home place.

However, I must say I agree with other commenters who are saying it will be near-impossible. If you are unaware of their domicile and they are a distant relative, then your chances of being granted access to these documents is slim even if you can locate them. The Japanese officials take personal information very seriously and do not release information about anyone normally unless they are the children or parents of the individual.

Anyways, it sounds like a complicated process ahead of you if you choose to continue looking for it. Good luck either way.

What do you know about your grandma, then? You can try to gather all the information you can obtain about her to track down the information you really want.

For example, I dug into ancestry websites where I found the boarding list of the ships my ancestors boarded. From the list I was able to find addresses and names of people surrounding them, which helped me do the next thing.

Here is another example of someone who tracked down her roots.
https://yokosuka1953.com/