The church was raised in the middle or later part of the twelfth century on the highest point of the parish, originally consisting of a nave, a narrower chancel and an eastern apse, all beneath a flat timber roof. Towards the end of the thirteenth century a tower of roughly hewn granite was added, later heightened in brick around 1400 and given stepped gothic gables. A porch was subsequently built against the nave's south side, where medieval men were required to leave their weapons before entering; it was later enlarged and given its own gothic gable, while a corresponding women's porch to the north was demolished in 1682.
Around 1300 the nave and chancel received brick rib vaults, and in the fifteenth century the chancel was lengthened, with the old apse and south wall removed and a new, squarer east end built. Further changes came in the nineteenth century: between 1815 and 1817 the church was extended northwards by incorporating an adjoining building, and around the mid-1800s the main entrance moved from the south porch to the tower's west side, after which the old porch became a sacristy. Two round-arched windows from the original medieval building survive, one in the nave wall and one in the chancel.
By the late 1800s the parish had built a new church at Arlöv, and the old church at Burlöv was allowed to fall into some neglect, with services reduced for a time. A restoration in 1908–09, led by Theodor Wåhlin, uncovered medieval limework paintings in the nave, porch and chancel that had been whitewashed over since the seventeenth century. The nave and porch paintings date from the 1200s–1300s and those in the chancel from the 1400s, characterised by simple foliage ornament, geometric patterns on the vault ribs and imitation ashlar work, in yellow, red and pale grey.
Among the furnishings, the oldest is a sandstone font from the 1200s, shaped like a contemporary communion chalice; it was removed to the churchyard at one point, lost part of its bowl, and was only fully reconstructed to its original form in 1959. The wooden altarpiece, made in Lund in 1598 in Renaissance style, was paid for by the Lund cathedral dean Wilhelm Dresselberg; its authorship has been attributed at different times to the carver Jacob Kremberg and, more recently, to the workshop of the so-called Köpinge Master. It is built in four tiers with biblical scenes and carved female figures said to represent virtues such as love, hope, faith, moderation and righteousness. The pulpit, from around 1600 and also Renaissance in style, was likewise funded by Dresselberg and features carved figures of the four evangelists.
The churchyard retains its old eastern and western boundaries, though it was extended in the nineteenth and early twentieth centuries. Part of its perimeter wall, particularly the older eastern stretch of granite, is thought to be of medieval origin. A handful of older gravestones, including one possibly from the 1500s bearing only a name and a merchant's mark, were built into the northern brick wall when it was constructed in the 1860s.