Imam Malik, may Allah have mercy on him, said: Those women who do not have husbands and have not performed Hajj, if they do not have a mahram or have one but he is unable to accompany them, then she should not abandon the obligatory Hajj, rather she should go for Hajj with other women.
It is narrated from Umm al-Mu'minin Sayyida Aisha (may Allah be pleased with her) that she used to say: Fasting is obligatory upon the person who performs tamattu', that is, performs 'Umrah and then Hajj, and does not find a sacrificial animal. He should fast from the time he enters into the state of ihram for Hajj until the day of 'Arafah. If he does not fast during these days, then he should fast during the days of Mina.
Hadith Referenceموطا امام مالك رواية يحييٰ / كتاب الحج / 957
Hadith Gradingمحدثین:موقوف صحيح
Hadith Takhrij«موقوف صحيح،أخرجه البيهقي فى«سننه الكبير» برقم: 8559، 8898، وأما حديث عائشة بنت أبى بكر الصديق أخرجه البخاري فى «صحيحه» برقم: 1999، فواد عبدالباقي نمبر: 20 - كِتَابُ الْحَجِّ-ح: 255»
Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) also said in this case the same as the statement of Sayyidah Aisha (may Allah be pleased with her).
Hadith Referenceموطا امام مالك رواية يحييٰ / كتاب الحج / 958