The Hungarian airline, founded in 2004 and which flew 13.9 million passengers last year, pulled plans to raise up to 200 million euros (£159 million) due to current market volatility in the airline sector.
A difficult few days saw German flag carrier Lufthansa cut profit forecasts for this year and next amid a warning over falling fares on its European and American routes.
A day later Irish flag carrier Aer Lingus issued its second profits warning this year after industrial action put passengers off booking with the airline.
The move by Wizz Air also follows a spike in oil prices to a nine-month high as turmoil in Iraq raised the threat of higher fuel bills for the airline sector amid broader concerns about slowing global economic growth.
Wizz Air said that despite a "positive response to it business story" it would not continue with the float, and gave no indication on when it might try again.
The airline, which flies to Liverpool, Luton and Doncaster/Sheffield airports, had planned to use the cash to launch routes and lease new aircraft.
Wizz said its outlook remained extremely positive and was unaffected by the decision not to proceed with the flotation.
Wizz Air's network spans 35 countries from 17 bases in nine central and Eastern European countries, with flights to 96 destinations on more than 315 routes.
Last month fashion retailer Fat Face pulled its float, citing "current equity market conditions".
The move comes after a rash of flotations earlier in the year, although the likes of Pets at Home and online retailer AO are now trading below their float prices and others such as Saga floated at the bottom end of their ranges.