The business, which has been majority owned by private equity firm Bridgepoint since 2007 and has former M&S boss Sir Stuart Rose as its chairman, said current market conditions were largely to blame for the decision.
Pets at Home, Poundland and Appliances Online have floated in recent weeks, while online property search firm Zoopla and discount chain B&M confirmed today their intention to join the stock market in the coming weeks.
Holidays-to-insurance firm Saga yesterday cut the target price on its flotation in order to ensure a positive aftermarket performance, although it said demand from retail investors had been "exceptional".
And Card Factory, which has more than 700 stores, now stands at 200p a share, valuing it at just under £700 million, after joined the market at 225p.
FatFace said it had decided to pull its offer despite a strong level of interest from institutional investors.
It added: "Current equity market conditions are the principal factor in the decision. The board remains confident in the prospects for the business and will continue to execute the growth plans which are already underway."
The company had planned to float a quarter of the business in a move expected to raise £110 million, giving a value of at least £400 million.