All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible for the Muslim woman to work as long as she abides by the rulings of the Shariah, as we have previously underlined in fatwa 82399.
If your wife is a righteous woman; observes the hijaab in the way which the scholars of Fiqh agreed upon, which is to cover her whole body except for the face and hands; and abides by decency when dealing with men if there is a need for it, then there is no harm on you in giving her permission to work.
The same applies to going to the market as long as the road to it is safe. If you could accompany her to the market, you should do so. It is up to you whether to allow women to visit her at home to buy from her; there is no religious impediment to allowing her to receive women in the house for that purpose.
We advise you to be keen on establishing your wife on Islam and faith and to organize religious gatherings and study circles at home. You can also accompany her to religious gatherings. Verily, the preservation of the righteousness of one's wife and children yields peace of mind and serenity in the man's heart.
Allah, The Exalted, says about the attributes of His chosen servants (what means): {And those who say: Our Lord, grant us from among our wives and offspring comfort to our eyes and make us an example for the righteous.} [Quran 25:74]
Ibn Katheer wrote, “Al-Hasan Al-Basri was asked about this verse and said, ‘It means that Allah makes the Muslim see his wife, his brother, and his close friend obeying Allah. Verily, there is no better comfort to the Muslim's eye than to see his child or grandchild or brother or intimate friend obedient to Allah.’”
Lastly, we would like to highlight that the scholars held different views regarding the ruling on covering the woman's face; the majority of the scholars held that it is recommended, while others held that it is obligatory. We incline to the second view, namely, that it is incumbent on the Muslim woman to cover her face. There is no doubt, though, that the difference of opinion on such matters is tolerated. For more benefit, please refer to fatwa 83033.
Allah knows best.