Short answer
Saying "Jummah Mubarak" (a blessed Friday) as a kind wish is permissible, because Friday really is a blessed day. It is not a sunnah, though: there is no report of the Companions greeting each other with it. Scholars warn against treating it as a religious ritual or a required greeting; said casually now and then, there is no harm.
There is no text from the early Hanafi imams on this phrase. Hanafi muftis generally say that saying it occasionally as a good wish is allowed, as scholars allowed congratulating one another on Eid, but treating it as a sunnah or a fixed weekly ritual is not supported and should be avoided, since adding practices to the religion is rejected.
The four schools agree on this.
Explanation
"Jummah Mubarak" means "may your Friday be blessed". Friday is the best day of the week: Adam was created on it, and the Hour will come on it. Wishing someone a blessed Friday is a form of du'a, and du'a for a fellow Muslim is good.
The question is whether it is a sunnah. It is not. Neither the Prophet ﷺ nor the Companions are reported to have greeted each other with it every Friday. A practice becomes a bid'ah (blameworthy innovation) when people treat it as part of the religion, believe it carries special reward, or blame those who do not do it. That is the line scholars draw.
- Fine: saying it now and then as a friendly wish or du'a.
- Avoid: treating it as a sunnah, a required weekly ritual, or something that earns special reward.
- Forwarding chains: mass messages that promise reward for sharing have no basis.
Some scholars are stricter and call the habitual greeting a bid'ah; others see no harm in it at all. This is a difference among later scholars rather than between the four schools, and the middle position above is what many Hanafi muftis give.
Better ways to honour Friday are the ones the Prophet ﷺ taught: ghusl, salawat, Surah al-Kahf, and du'a in the last hour. See the sunnahs of Friday and why Jummah is on Friday.
The evidence
Sahih Muslim 854
Sahih... خير يوم طلعت عليه الشمس يوم الجمعة فيه خلق آدم ...
"The best day on which the sun rises is Friday; on it Adam was created."
Friday is a blessed day, so wishing someone its blessing is meaningful.
Sahih al-Bukhari 2697
Sahih... من أحدث في أمرنا هذا ما ليس فيه فهو رد ...
"Whoever introduces into this affair of ours what is not part of it, it is rejected."
Practices must not be added to the religion as if they were sunnah.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, chapter on the Eid prayer. Congratulating one another on Eid is permissible, which scholars extend to good wishes on blessed days.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.