The church was built towards the end of the 1100s in Romanesque style, with a tower on its western side. It probably shared its layout and proportions with the nearby Hilleshög church. Sånga is first mentioned in surviving documents in 1308, when a woman named Ingeborg bequeathed land to the church; a priest is also noted at that time.
During the 1300s the church was extended eastward into a hall church, and a sacristy with a cross-vaulted ceiling was added, giving the east end its straight-ended wall. Between about 1430 and 1470 a porch was added on the south side and the nave itself received cross vaults. Medieval murals survive from this long building history. The present tall spire dates from 1730, replacing an earlier one from the 1500s destroyed by a lightning strike.
Among the fittings, the stone font is contemporary with the church itself, made in two pieces with drainage holes. The pulpit, in late Renaissance style, was made in 1635 in northern Germany. A notable memorial tablet from 1584, bearing a landscape painting, is considered one of the oldest of its kind in Sweden.
The church's organ history is unusually eventful: an instrument originally built in 1797 for Lovö church was moved to Sånga in 1885, later removed and stored during a 1964 restoration, relocated to Skå church in 1968, then brought back to Sånga and restored in 2010. A separate mechanical organ, built in 1965, also serves the church.
The churchyard is entered through two lychgates in its surrounding wall, one dating from the later 1400s and the other from 1674. About a hundred metres east of the church stands a detached bell tower built in 1949, replacing an earlier 18th-century structure that burned down.