The artist was presented with the £25,000 prize by actor James Norton at Tate Britain on Tuesday evening.
She beat fellow shortlisted nominees Pio Abad, Claudette Johnson and Delaine Le Bas.
Kaur’s exhibition includes family photos, an Axminster carpet, a vintage car covered in a giant doily and kinetic handbells.
Turner Prize organisers noted Kaur’s work explores how cultural memory is layered in the objects and rituals that surround us.
The judges said Alter Altar “reflects upon everyday objects, animating them through sound and music to summon community and cultural inheritance”, resulting in a “visual and aural experience that suggests both solidarity and joy”.
Kaur studied silversmithing and jewellery at Glasgow School of Art in 2008, before moving to London to study at the Royal College of Art the following year.
Her work has previously been showcased at the Victoria and Albert Museum. Her short film Yoorop showed an account of Europe using footage from popular Indian cinema.
It was intended to show an image of European-ness from an alternative cultural perspective.