Praise be to Allaah.
Yes, it is prescribed for him to say al-hamdu Lillah, because
it is proven in the saheeh hadeeth that the Prophet (peace and
blessings of Allaah be upon him) heard someone say al-hamdu Lillah after
sneezing and he did not rebuke him, rather he said: “I saw such and such a
number of angels, all of whom were hastening to write it down.” And because
praising Allaah is akin to the phrases of prayer, and is not contrary to
it.” End quote.
Majmoo’ Fataawa al-Shaykh Ibn Baaz (29/348).