Narrated Abu Burdah: The Jews used to try to sneezes in the presence of the Prophet ﷺ hoping that he would say to them: "Allah have mercy on you!" but he would say: May Allah guide you and grant you well-being!
Related hadith on this topic
Explanation & Benefits
Shaykh Umar Farooq Saeedi
Benefits and Issues:
To a non-Muslim, in response to his sneeze, instead of saying (yarhamuk Allah), one should say (yahdikum Allah wa yuslih balakum), just as one cannot initiate (as-salamu alaykum) to him. And if he says it, then in reply only "alaykum" is said.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 5038
Shaykh Dr. Abdur Rahman Freywai
Explanation:
1:
From this hadith, it is understood that in response to the sneeze of non-Muslims, only (yahdikumullahu wa yuslihu balakum) should be said.
And (yarhamukumullah) ("may Allah have mercy on you") should not be said, because the mercy of Allah in the Hereafter is exclusively for Muslims.
Source: Sunan al-Tirmidhi – Majlis ‘Ilmi Dar al-Da‘wah, New Delhi Edition, Page: 2739