Al-Imaam Shaykh Muhammad Ibn Saalih Al-Uthaymeen (may Allaah have mercy upon him) stated:
"From the capability (a condition for one to make Hajj) is that the woman finds for herself a Mahram (non-marriageable kin or husband). If she doesn't have a Mahram for herself (to travel with her), in this case, the Hajj is not obligatory upon her. However, the scholars differ, is it obligatory upon her in this situation for her to send someone who will make the Hajj or Umrah on her behalf or not?
There are two statements from the scholars regarding this, based upon whether the presence of the Mahram is a condition for the obligation of performance, or is it a condition for the obligation itself. That which is well-known from the scholars of the Hanbali school of jurisprudence, May Allaah have mercy upon them, is that the Mahram is a condition for the obligation itself and that the woman who doesn't have a Mahram (to travel with her), then the Hajj is not obligatory upon her nor is it upon her to send someone to make the Hajj on her behalf.
These are the five conditions for the Hajj to become obligatory (upon a person): Islaam, Sound Mind, Puberty, Free (not a slave), and Capability. These condition includes both Hajj and Umrah."
Taken from Fiqhul-'Ebaadah pg. 308-309
Sisters Upon Al-Istiqaamah