It was narrated that 'Aishah said:

"When the Messenger of Allah ﷺ wanted to observe I'tikaf, ^[1] he would pray Fajr then enter the place where he wnated to observe I'tikaf. He wanted to observe I'tikaf during the last ten days of Ramadan, so he commanded that a Khiba' (tent) ^[2] be pitched for him. Then Hafsah ordered that a Khiba' be pitched for her, and when Zainab saw her tent she ordered that a Khiba' be pitched for her too. When the Messenger of Allah ﷺ saw that he said: 'Is it righteousness that you seek?' And he did not observe I'tikaf in Ramadan, and observed I'tikaf for ten days in Shawwal (instead)."

[1] Seclusion in the Masjid for the sake of devotion to Allah
[2] Al-Khiba': "One of the house of the Bedouins made of Wabir (camel or goat fur) or wool, not of hair (from other pelts). And it would have two or three posts." (An-Nihayah)

أَخْبَرَنَا أَبُو دَاوُدَ، قَالَ حَدَّثَنَا يَعْلَى، قَالَ حَدَّثَنَا يَحْيَى بْنُ سَعِيدٍ، عَنْ عَمْرَةَ، عَنْ عَائِشَةَ، قَالَتْ كَانَ رَسُولُ اللَّهِ ﷺ إِذَا أَرَادَ أَنْ يَعْتَكِفَ صَلَّى الصُّبْحَ ثُمَّ دَخَلَ فِي الْمَكَانِ الَّذِي يُرِيدُ أَنْ يَعْتَكِفَ فِيهِ فَأَرَادَ أَنْ يَعْتَكِفَ الْعَشْرَ الأَوَاخِرَ مِنْ رَمَضَانَ فَأَمَرَ فَضُرِبَ لَهُ خِبَاءٌ وَأَمَرَتْ حَفْصَةُ فَضُرِبَ لَهَا خِبَاءٌ فَلَمَّا رَأَتْ زَيْنَبُ خِبَاءَهَا أَمَرَتْ فَضُرِبَ لَهَا خِبَاءٌ فَلَمَّا رَأَى ذَلِكَ رَسُولُ اللَّهِ ﷺ قَالَ " آلْبِرَّ تُرِدْنَ " . فَلَمْ يَعْتَكِفْ فِي رَمَضَانَ وَاعْتَكَفَ عَشْرًا مِنْ شَوَّالٍ .