The bill passed the opposition-led parliament last month, prompting protests from some medical workers who said the new law would open the door for nurses to provide treatment without a medical license.
Nurses say that the doctors' claim is groundless, and that the country needs more care centres to cope with its rapidly aging population.
In vetoing the bill, Yoon said that the new law caused excessive conflict among medical workers, and that nursing practices outside medical institutions would cause public anxiety over the healthcare system.
The Korean Nurses Association, which led the walkout, strongly denounced Yoon, saying he abandoned his promise as a presidential candidate to improve nurses' working conditions.
The impact of the strike was seen as limited so far, as most protesters used holiday time or shortened business hours, with major hospitals operating normally.