According to the power station's website, the utility company (Sydkraft) that built and operated the plant purchased the land in 1965 from a seller named Count Ian Hamilton, who owned an estate at that location. The site was favorable for several reasons, including:

...few people live[d] within a 5-kilometer zone around the planned work, a single landowner, proximity to the existing 400 kV lines and electricity customers as well as the ability to supply hot water to Lund and Malmö.

(Translation via Google.)

Also note that nuclear plants always need to be built near large bodies of water.

Additionally, some Danish officials may have seen advantages to having the plant near Copenhagen, according to the UNH School of Law's IP Mall:

From the period when Sydkraft... presented the plans of a nuclear power station in 1968 to granting planning permission in 1970, Danish policy makers raised no objections. The lack of opposition may be partly explained by Danish plans for nuclear power. Until the mid-70's, Danish policy makers had considered building nuclear reactors of their own, and when Barsebäck was being built, Sydkraft signed several electricity transfer deals with their Danish counterparts.