Question
Are women allowed to be Hindu sanyasis/monks?
Answer
Yes woman are allowed to become monks/sanyasinis/rishikas.
Hinduism is probably the only living religion which considers God to be feminine. And in ancient times many vedic rishis were women.
The notable female rishikas who contributed to the composition of the Vedic scriptures are: The Rig Veda mentions Romasha, Lopamudra, Apala, Kadru, Visvavara, Ghosha, Juhu, Vagambhrini, Paulomi, Yami, Indrani, Savitri, and Devayani. The Sama Veda adds Nodha, Akrishtabhasha, Sikatanivavari and Gaupayana.1
Another famous female monk was Andal who is revered by Tamil Vaishnavites.
In today's time, as mentioned by @Pradip Gangopadhyay, Ramakrishna Sarada math and Mata Amritanandamayi are examples.
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