First, of the Greek world, we have the Catalogue of Women (sometimes called the Ehoiai). This is a debatable entry, as it lacks a strict narrative. Instead, it's the account of the birth of heroes traced through their mothers. I mention it because there is a close relationship between ancient Greek genealogical poetry and Greek narrative poetry.
Better though would be the Europia and Danaides.
Unfortunately, nothing substantial exists from the Europia. It was an epic poem supposedly composed by Eumelus of Corinth in the 8th century about Europa, the Phoenician princess and sister of Cadmus (who later founded Thebes in search of her) who was abducted by Zeus. How much of her character is developed is unknown.
Like the Europia, the Danaides is also mostly lost. However, unlike Europia and like the Catalogue of Women, it was probably genealogical in nature, though the focus was on the Daughters of Danaus.
For more on these two, I recommend checking out Martin West's Greek Epic Fragments from the Loeb Library.
Moving away from Greek works, we have a few of these in the Tamil tradition. The first one is the Kundalakesi. Unfortunately, like the ones prior, it too is only excerpted and not fully preserved. Wikipedia preserves a summary:
Kundalakesi is an adaptation of the story of the Buddhist Bhikṣuni (lit. female monk) Kunḍalakeśi from the Dhammapada. The protagonist Kundalakesi (lit. The woman with curls) was born in a merchant family in the city of Puhar. Her birth name is "Bhadra". She loses her mother during childhood and lives a sheltered life. One day she sees a thief being paraded in the streets of Puhar and falls in love with him. The thief, Kaalan has been sentenced to death for banditry. Besotted with Kaalan, Kundalakesi implores her father to save him. Her father petitions the king for the thief's release. He pays Kaalan's weight in gold and 81 elephants to the treasury to secure Kaalan's release. Kundalakesi and Kaalan are married and live happily for some time. One day, she playfully refers to him as a thief. This enrages the mercurial Kaalan and he decides to kill his wife in revenge. He tricks her into visiting the summit of the nearby hill. Once they reach the summit, he announces his intention to kill her by pushing her off the hill. Kundalakesi is shocked and asks him to grant a final wish – she wishes to worship him by going around him three times before she dies. He agrees and when she gets behind him, Kundalakesi pushes him off the summit, killing him. Repenting her actions, she becomes a Buddhist monk and spends the rest of her life spreading the teachings of Buddha. She carries out theological battles with Jains and Hindus, defeating them in debates. She finally attains superior liberation. In one of the versions, it is believed that she was a Jain in her initial life and she shattered conventions by becoming a nigrantha or naked monk.
The Neelakesi was written in response to the Kundalakesi. Instead of a Buddhist nun, it tells the story of
the Jain nun [Neelakesi] who was a rival of the Buddhist protagonist of the Kundalakesi. According to the epic, when animal sacrifices of a temple of the Kali in Panchala were stopped due to the influence of the Jains, the Goddess dispatched the local deity Nīli to seduce and destroy the monk responsible for it. However, Nīli herself is converted to Jainism by the monk. Nīlakēci, as she is renamed, travels the country indulging in philosophical debate with rhetoricians of other religions. She debates and defeats several Buddhist rhetoricians like Arkachandra, Kundalakesi, Moggallana (Tamil: Mokkala) and even Gautama Buddha himself.
The third Tamil epic is the Silappatikaram, which is about "Kannagi, who having lost her husband to a miscarriage of justice at the court of the Pandyan Dynasty, wreaks her revenge on his kingdom."
The final Tamil epic with a female protagonist is the Manimekalai, a sequel to Silappatikaram. It "describes how Manimekalai, the beautiful daughter of Kovalan and Madhavi, follower of local deities later included in Hinduism, converts to Buddhism."
If we do not limit it to the ancient world, Elizabeth Barret Browning in 1865 published Aurora Leigh, an epic in 9 books written in blank verse. Wikipedia explains:
It is a first person narration, from the point of view of Aurora; its other heroine, Marian Erle, is an abused self-taught child of itinerant parents. The poem is set in Florence, Malvern, London, and Paris. She uses her knowledge of Hebrew and Greek, while also playing off modern novels, such as Corinne ou l'Italie by Anne Louise Germaine de Staël and the novels by George Sand.
There were other ancient tales that aren't strictly epic poems that featured a woman as the lead figure, such the Aramaic text of Esther (Heb. אֶסְתֵּר) found in both Jewish and Christian bibles, and Judith, a deuterocanonical book found in the Catholic and Orthodox bibles.