Short answer
No, Muslims do not worship the Kaaba. They worship Allah alone. The Kaaba is the House built by Ibrahim (Abraham) and Ismail for the worship of Allah, and the direction (qiblah) Muslims face in prayer. Walking around it is worship of Allah done at a place He chose.
Worship of anything besides Allah is shirk and leaves Islam. Facing the Kaaba is a condition of the validity of salah, and tawaf around it is a rite of Hajj and umrah, both done for Allah alone. The four schools agree.
The four schools agree on this.
Explanation
Muslims believe the Kaaba is the first house set up on earth for the worship of Allah. The Quran says Ibrahim and Ismail raised its foundations and prayed for it to be accepted. It is a plain cube of stone covered with a black cloth (the kiswah); there is no idol, image or object of worship inside.
Why face it? Allah commanded the believers to turn their faces toward the Sacred Mosque in prayer. Facing one point unites Muslims across the world in one direction; it does not mean the building hears or answers prayers. The Quran's words are "worship the Lord of this House", not the House itself. See why Muslims face Makkah.
The Black Stone: when Umar ibn al-Khattab kissed it, he said aloud that he knew it was a stone that could neither harm nor benefit, and that he kissed it only because he had seen the Prophet ﷺ do so. That sentence sums up the Muslim view of the whole House. See why Muslims kiss the Black Stone.
Before the Kaaba was the qiblah, Muslims faced Jerusalem, and if the building were ever gone, Muslims would still face its place. That shows the direction is an act of obedience, not a cult of the building. More on its history is in Kaaba facts.
The evidence
Quran, Surah Quraish 106:3
فَلْيَعْبُدُوا۟ رَبَّ هَٰذَا ٱلْبَيْتِ ﴿٣﴾
Let them worship the Lord of this House,
Worship is for the Lord of the House, not the House.
Quran, Surah Al-Baqara 2:144
قَدْ نَرَىٰ تَقَلُّبَ وَجْهِكَ فِى ٱلسَّمَآءِ ۖ فَلَنُوَلِّيَنَّكَ قِبْلَةًۭ تَرْضَىٰهَا ۚ فَوَلِّ وَجْهَكَ شَطْرَ ٱلْمَسْجِدِ ٱلْحَرَامِ ۚ وَحَيْثُ مَا كُنتُمْ فَوَلُّوا۟ وُجُوهَكُمْ شَطْرَهُۥ ۗ وَإِنَّ ٱلَّذِينَ أُوتُوا۟ ٱلْكِتَٰبَ لَيَعْلَمُونَ أَنَّهُ ٱلْحَقُّ مِن رَّبِّهِمْ ۗ وَمَا ٱللَّهُ بِغَٰفِلٍ عَمَّا يَعْمَلُونَ ﴿١٤٤﴾
We have certainly seen the turning of your face, [O Muhammad], toward the heaven, and We will surely turn you to a qiblah with which you will be pleased. So turn your face toward al-Masjid al-Haram. And wherever you [believers] are, turn your faces toward it [in prayer]. Indeed, those who have been given the Scripture well know that it is the truth from their Lord. And Allah is not unaware of what they do.
Facing the Kaaba in prayer is a command from Allah.
Quran, Surah Aal-i-Imraan 3:96
إِنَّ أَوَّلَ بَيْتٍۢ وُضِعَ لِلنَّاسِ لَلَّذِى بِبَكَّةَ مُبَارَكًۭا وَهُدًۭى لِّلْعَٰلَمِينَ ﴿٩٦﴾
Indeed, the first House [of worship] established for mankind was that at Makkah - blessed and a guidance for the worlds.
The Kaaba is the first house of worship of Allah.
Sahih al-Bukhari 1597
Sahih... إني أعلم أنك حجر لا تضر ولا تنفع ...
"Umar said to the Black Stone: I know you are a stone that neither harms nor benefits, and had I not seen the Prophet kiss you, I would not have kissed you."
Honouring the Kaaba is following the Sunnah, not worshipping stone.
Where the ruling is recorded
- al-Hidaya, Kitab al-Salah, chapter on the conditions of prayer. Facing the qiblah is a condition of salah.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, on facing the qiblah. The qiblah is the place of the Kaaba, not the building itself.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.