Muslims are only allowed to bow and prostrate to God because we consider such things acts of worship, and Islam is a very monotheistic religion.
This is a problem in Japan, where bowing is considered a common greeting.
How do I handle greetings where I'm expected, but unable to bow, without seeming disrespectful?
As an American with a strong interest in Japan and Japanese culture I think that you will be fine without bowing. This is second-hand advice, so definitely don't treat it as the final word.
Bowing in Japan is (as far as I am aware) a lot more intricate than just bending at the waist to some arbitrary angle. Advice that I have received as someone travelling to Japan (and that I have seen given to other travelers) is to not bother trying to bow. It's apparently just very difficult to appreciate all of the nuances and implications as an outsider, and so even if you were to bow there is a good chance that you're doing it "wrong" in some way or another (though probably not to any horrifying extent, just not exactly correct for your situation).
Japan is an interesting place, but it's very used to tourists and other travelers that don't really understand the intricacies of Japanese culture. Especially if you're in a larger city any good-faith effort to be polite will likely be received well (they were certainly accommodating of and kind about my poor-quality Japanese language skills).
Shaking hands is supposed to be getting more popular there, especially for businesspeople, but is still unusual. If you're there for business purposes you'll be better off reading up on customary business card exchange (it's a real thing, and there are rules for it) than worrying about bowing or not. And if you're there just to visit, the standard of behavior expected of you will be quite low. Honestly, by worrying about this at all you are probably ahead of the game compared with any random tourist.
This is only my "preference" for handling such a situation.
I posed the question as if I were unable to greet someone with a handshake either due to a medical condition or religious constraint (I believe certain Jewish holy men can not touch).
I would smile very happily, and either nod or wave. i.e. A different cue that I am happy to see that individual and I acknowledged his presence. I would explain only if pressed or the other person appears sad. Perhaps a cue also that I am not able to shake hands (or in your case bow)?
Note I am from United States, and I do realize Japanese society is quite different, so I am not sure if they would react as other Americans would given the above.
Nice Question
In short,
Further explanation -
Bowing means doing Ruku (putting at 90 degrees) or doing prostrating means doing Suju (completely down, putting your fore-head down) is Haram (not allowed) in Islam. You can only bow down and do Suju to Allah (God) and no one else.
Sitting down is not Haram. But a person you want to show as superior and want to degrade you and sit down i.e. not good in Islam. This is against to Islamic culture. All the human being are equal in Islamic culture.
Allah said in Surah Al Hujuraat Ayat (Quran Ch.49 V.13) -
"Human beings, We created you all from a male and a female, and made you into nations and tribes so that you may know one another. Verify the noblest of you in the sight of Allah is the most God-fearing of you. Surely Allah is All-knowing, All-Aware."
In short, you can sit down to greet the people in Japan.
Japanese people are friendly, they can understand the fact that the greetings against the religion's rule is prohibited and it will not be considered as disrespectful act. Here, your intention behind 'not bowing' is pure and there is specific reason. You have respect for them in your mind and that solves the problem.
The handshake is globally accepted body language.
