The photos posted show the little girl drinking from the cup, shots of Mr Zuckerberg’s Shabbat candles and some homemade challah.
With wife Priscilla Chan, Mr Zuckerberg has two children – Max and August, who was born last month.
Although the Facebook co-founder had in the past proclaimed himself to be an atheist, last year he said he recently realised the importance of faith and tradition.
In December he wrote: “I was raised Jewish and then I went through a period where I questioned things, but now I believe religion is very important.”
Giving the commencement address at Harvard University earlier this year, he told graduates that he sings the ‘Mi Shebeirach’ prayer to his daughter every night.