Yes, Muslims can say "God bless you."
While "God bless you" is a common expression in English, often used as a response to someone sneezing, Muslims can use similar phrases rooted in Islamic tradition and language. In Arabic, a common equivalent to "God bless you" is expressed in several ways depending on the context. Here are a few examples:
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Responding to a sneeze: While there isn't a direct equivalent to "God bless you" after a sneeze, the tradition in Islam is that the person who sneezes says "Alhamdulillah" (Praise be to God). Those who hear it should then respond with "Yarhamukallah" (May God have mercy on you). The sneezer then replies "Yahdikumullahu wa yuslihu balakum" (May God guide you and set your affairs right).
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Responding to congratulations or compliments: You can say "الله يبارك فيك" (Allah yubarik feek) to a male or "الله يبارك فيكي" (Allah yubarik feeki) to a female. This translates to "May God bless you."
Therefore, the concept of wishing blessings from God is present in Islamic culture, just expressed through different phrases. There's no prohibition against using "God bless you" in English, and it can be considered an acceptable way to express goodwill.