The hadith you are referring to is a da'īf (weak) hadith mawqūf, which means that the narration (hadith) is attributed to a companion, not to the Prophet ﷺ (mawqūf). In our case here, the narration you are asking about is attributed to 'Abdullah ibn 'Abbas (others have narrated this hadith, too).
This hadith is documented in multiple books, for example in Tafsir at-Tabari 20/324 (Arabic only) by At-Tabari in his commentary on Surat Al-Ahzab 33:59:
عن ابن عباس قوله ❬ يَا أَيُّهَا النَّبِيُّ قُل لِّأَزْوَاجِكَ وَبَنَاتِكَ وَنِسَاءِ الْمُؤْمِنِينَ يُدْنِينَ عَلَيْهِنَّ مِن جَلَابِيبِهِنَّ ❭ أمر الله نساء المؤمنين إذا خرجن من بيوتهن في حاجة أن يغطين وجوههن من فوق رءوسهن بالجلابيب ويبدين عينا واحدة
— NOTE: My own translation, so treat with care:
Narrated by Ibn 'Abbas that he said: "In His saying 'O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments,' Allah commanded the women of the believers, if they leave their homes to run an errand, that they cover their faces from the top of their heads with their outer garments, and to show only one eye."
This hadith mawqūf is narrated through 'Ali ibn Abu Talha through Abu Sāleh through Mu'āwiya ibn Abu Sufyān through 'Ali ibn Abu Tālib through 'Abdullah ibn 'Abbas. This narration chain was deemed da'īf by Ibn Taymiyyah as documented by Sa'īd ibn 'Ali al-Qahtāni in Idhhār al-Haq wa as-Sawāb 2/95 (Arabic only) due to the fact that it is severed. In Ar-Radd al-Mufhim pp. 48, the same hadith mawqūf was deemed da'īf by Muhammad Nasiruddin al-Albani.
It is worth noting that there are other scholars who have deemed this hadith sahih (authentic), e.g., Ibn Abu Shaybah.
Note. This answer is meant to address the question about the authenticity of this particular narration. It is not to be taken as a ruling on whether covering the face is mandatory or recommended for a woman when going out of her house.