The position of the majority of scholars is that it is not permissible. ʿĀʾishah reported that the Prophet ﷺ took the pledge of allegiance from the women by words alone, and that "the hand of the Messenger of Allah ﷺ did not touch the hand of any woman" in that pledge (Ṣaḥīḥ al-Bukhārī 7214). This is decisive because the pledge itself was commanded in the Quran (Quran 60:12) — if contact were permissible anywhere, it would have been permissible in an act of obedience the Prophet ﷺ was ordered to accept. He also told the women who came to pledge to him plainly, "I do not shake hands with women" (Sunan Ibn Mājah 2874, ṣaḥīḥ). It falls under the general command to both sexes to lower the gaze and guard their chastity (Quran 24:30-31). Some jurists made an exception for an elderly woman in whom there is no attraction, but the safest and best-evidenced course is to decline politely — a hand placed over the heart with a warm greeting — and to explain that it is a matter of religion, not of disrespect.
Q&A · Women in Islam
Is it permissible for a woman to shake hands with a non-mahram man?
Evidence — the daleel
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.