Downer will pay £24m in cash for the stake when the deal completes in early 2019.
KHSA, which was acquired as part of the Mouchel group of companies in 2015 reported £7m profit last year and has total assets of £52m.
Proceeds from the sale will be used to accelerate the reduction of Kier’s net debt.
Kier is aiming to raise up to £50m from non-core business disposals as part of a plan to cut its debt mountain of £375m.
Two months ago Kier has sold its third-party pension management business for £3.5m.
Alongside £20m annual savings from its Future Proofing Kier streamlining programme, the group aims to reduce debt to £250m and be in a net cash position by 2021.