The church was designed by architect Johannes Olivegren, who won a competition organised by the so-called small church movement, a mid-century initiative encouraging the building of modest district churches in Sweden's expanding towns and suburbs. Björkekärrs kyrka is said to have been consecrated on Whit Sunday in 1958.
The building is constructed of dark red brick and is arranged as four linked sections: a church hall, nave and chancel, and an attached bell tower with a sacristy beneath. These parts are staggered against one another and set at differing heights, giving the exterior an irregular, layered profile typical of Nordic modernism.
Inside, the dominant feature is the chancel's large mosaic window, running from floor to ceiling, which serves both as an exterior decorative element and as the church's altarpiece. It was created by the artist Ralph Bergholtz. The interior walls and floors are faced with brick in varying shades, giving the space a textured, living quality.
The church's origins lie in the reorganisation of Gothenburg's parish boundaries in 1951, when Härlanda parish was formed and new district churches were built to serve the city's growing suburbs. Björkekärrs kyrka has since been extended on more than one occasion, and today forms its own parish within Örgryte pastorate.
The church has had more than one organ: an instrument originally transferred from Härlanda kyrka in 1960 was later moved on to Brännö kyrka in 1987, when a new mechanical organ was installed in its place.