It is haraam for a woman to wear false eyelashes because they come under the heading of hair extensions, for which the Messenger of Allah (peace and blessings of Allah be upon him) cursed those who do that.
Al-Bukhaari and Muslim (2122) narrated that Asma’ bint Abi Bakr said: A woman came to the Prophet (peace and blessings of Allah be upon him) and said: “O Messenger of Allah, I have a daughter who is newly married, and she had the measles and her hair fell out. Can I give her hair extensions?” He said: “Allah has cursed the one who fixes hair extensions and the one who has that done.”
Al-Bukhaari (5205) and Muslim (2123) narrated from ‘Aa’ishah that a girl from among the Ansaar got married and she became sick and her hair fell out. They wanted to give her hair extensions, so they asked the Messenger of Allah (peace and blessings of Allah be upon him) about that, and he cursed the one who fixes hair extensions and the one who has that done.
The one who fixes hair extensions is the one who joins the other hair to the woman’s hair. The one who has that done is the woman who asks someone else to do that for her. These ahaadeeth clearly state that it is haraam to fix hair extensions, and the one who fixes hair extensions and the one who has that done are both cursed in general terms. This is the more correct meaning.
False eyelashes come under the same heading, because the real eyelashes are extended with the false ones.
Moreover, some doctors have mentioned that false eyelashes lead to chronic allergies in the skin and eyes, and to infection in the eyelids, and may cause the eyelashes to fall out. So using them is harmful, and the Lawgiver forbids that as the Prophet (peace and blessings of Allah be upon him) said: “There should be neither harming nor reciprocating harm.”
The Muslim woman should note that paying too much attention to such matters may be a kind of over-indulgence in leisure and luxury, and a waste of time and money which she could have used for something more beneficial to the Muslims, especially nowadays when people have no drive to do good and women have been distracted from their basic role which is to raise the next generation, and instead they are paying too much attention to these matters.
And Allah knows best.
(Source - Islam Q&A)