A Muslim recently asked me whether a devout Muslim (i.e., a Muslim who completely and firmly both believes and practices Islam) is fulfilling all 7 laws of Noah. So does a person who believes in Muhammed as a prophet, the Quran as sacred text, follow shariah law, etc. - is such a Muslim fulfilling all 7 laws of Noah (with special concentration on the first 2 laws as they are usually given)?
I am not a great scholar on Islam laws so I can't tell you what is in the Shariah or the different Islamic practices. The seven Noahide laws are: Idolatry Adultery Murder Not eating a limb of a life animal Not to blaspheme G-d Theft Establishing a just court system Maimonides (Sanhedrin 8; 11) teaches that in order to be a "Chassid" i.e. a pious gentile he has to accept these seven laws upon himself as the seven laws of G-d and not just happen to do them of his own accord. As for the question whether Islam is defined as idolatry or not – the Rambam (Maachalot 11; 7) holds they aren't and that's the common understanding today, though that does not necessarily mean that you are allowed to practice Islam or for your matter – that he is not transgressing the first of the Noahide laws. (See Responsa Divrei Yatziv YD 40)