Grading: Its isnad is sahih.

Corroborating chains and supporting reports: It was recorded by al-Bukhari (6792, repeated) from Uthman bin Abi Shaybah, and by Muslim (1685) from Muhammad bin Abd Allah bin Numayr, both of them from Humayd al-Ru'asi, with this same isnad.
Note / Clarification: Al-Hakim's mentioning it (in the Mustadrak) is an oversight on his part (because it is already in al-Bukhari and Muslim).

Corroborating chains and supporting reports: It was also narrated by al-Bukhari (6792), (6793) and (6794), Muslim (1685) and al-Nasa'i (7387) via several routes from Hisham bin Urwah.

Reference / Source: Al-Nasa'i (7362) narrated via Yunus, from Ibn Shihab (al-Zuhri), from Urwah, from A'ishah (may Allah be pleased with her), that the Messenger of Allah (peace and blessings be upon him) said: "The hand is not to be cut off except for the price of a shield, a third of a dinar or half a dinar, or more."

Details of the narration: Al-Nasa'i (7384) and (7385) narrated via Makhramah bin Bukayr bin Abd Allah bin al-Ashajj, from his father, from Uthman bin Abi al-Walid, the mawla of the Akhnasis, from Urwah bin al-Zubayr, who said: A'ishah (may Allah be pleased with her) used to narrate from the Prophet (peace and blessings be upon him) that he (peace and blessings be upon him) would say: "The hand is not to be cut off except for (stealing) a shield, or its price." In the second narration there is the addition that Urwah said: The shield is (worth) four dirhams.

Details of the narration: Al-Nasa'i (7378) narrated via Muhammad bin Abd al-Rahman bin Abi al-Rijal, from Amrah, from A'ishah (may Allah be pleased with her), that the Messenger of Allah (peace and blessings be upon him) said: "The thief's hand is to be cut off for the price of a shield", and the price of a shield was a quarter (1/4) of a dinar.

Details of the narration: Al-Nasa'i (7382) narrated via Sulayman bin Yasar, from Amrah bint Abd al-Rahman, that she heard A'ishah (may Allah be pleased with her) say: The Messenger of Allah (peace and blessings be upon him) said: "The thief's hand is not to be cut off for less than (the price of) a shield." A'ishah was asked: What is the price of a shield? She said: A quarter of a dinar.

Details of the narration: Al-Bukhari (6790), Muslim (1684) (2), Abu Dawud (4384), al-Nasa'i (7364) and Ibn Hibban (4455) and (4460) narrated via Yunus bin Yazid, from Ibn Shihab, from Urwah and Amrah, from A'ishah (may Allah be pleased with her), from the Messenger of Allah (peace and blessings be upon him), that he said: "The thief's hand is not to be cut off except for a quarter of a dinar or more"; (in this narration) there is no mention of the shield (mijann).

Note / Clarification: A "hajafah" is made of wood or bone and covered with leather, while a "turs" is like the hajafah except that two layers of leather are fitted on it.