The business, majority owned by private equity firm Bridgepoint since 2007 and with 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 yesterday confirmed their intention to join the stock market in the coming weeks.
Holidays-to-insurance firm Saga this week 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 now stands at 197.5p a share, valuing it at just under £700 million, after it joined the market at 225p.
FatFace said it had decided to pull its offer despite a strong level of interest from institutional investors.
The company had planned to float a quarter of the business in a move expected to raise £110 million, giving it an overall value of at least £400 million.
The flotation of Zoopla will enable shareholders, including majority owner Daily Mail & General Trust and founder Alex Chesterman, to realise some of their stakes and place a valuation of more than £1 billion on the business. B&M, which operates 373 stores in town centres and out-of-town locations, wants to raise £75 million towards reducing debt when it sells shares.