The airline, which focuses on the central and eastern European markets, said it will reduce flights from 11 March to countries affected by the virus - mostly to Italy - and is looking at cutting capacity by about another 10 per cent between April and June.
Wizz Air said a task force has been set up to "address the financial implications of Covid-19" since the start of the outbreak.
Measures taken include "significant" cutting of cost overheads and discretionary spending, pausing recruitment and non-essential travel, and working with suppliers to make further savings.
The London-listed Hungarian company did not estimate the size of the hit from the outbreak in the year to 31 March, adding that it is "difficult to predict the extent and the duration of the outbreak and the impact on the next financial year".
Chief executive Jozsef Varadi said: "Our ever-disciplined attitude to cost enables Wizz Air to partly offset some of the headwinds due to the Covid-19 outbreak, which have driven a temporary decline in demand and an increase in the cost of disruption as we put the well-being of passengers and crew first."
It comes after rivals have also cancelled flights and reined in routes in response to coronavirus.
British Airways owner International Airlines Group (IAG) said on Monday it was cancelling more than 400 flights, mostly on short-haul routes between Heathrow and Italy, France, Austria, Belgium, Germany, Ireland and Switzerland.
The airline had already suspended its flights serving mainland China and reduced the frequency of flights to northern Italy and Singapore.
Ryanair also said on Monday it was cancelling up to one in four flights on some of its routes, particularly those serving Italian airports, while other measures include "rolling schedule cuts", allocating leave or paid leave to pilots and cabin crew, working with suppliers to cut costs and freezing recruitment, promotion and pay across its network.
EasyJet had announced last week that it was cancelling some flights because of the coronavirus.