We present the results of a search for high-energy muon neutrinos with the IceCube detector in coincidence with the Crab Nebula flare reported on 2010 September by various experiments. Due to the unusual flaring state of the otherwise steady source we performed a prompt analysis of the 79-string configuration data to search for neutrinos that might be emitted along with the observed γ-rays. We performed two different and complementary data selections of neutrino events in the time window of 10days around the flare. One event selection is optimized for discovery of E -2ν neutrino spectrum typical of first-order Fermi acceleration. A similar event selection has also been applied to the 40-string data to derive the time-integrated limits to the neutrino emission from the Crab. The other event selection was optimized for discovery of neutrino spectra with softer spectral index andTeV energy cutoffs as observed for various Galactic sources in γ-rays. The 90% confidence level (CL) best upper limits on the Crab flux during the 10day flare are 4.73 × 10-11cm-2s -1TeV-1 for an E -2ν neutrino spectrum and 2.50 × 10-10cm-2s-1TeV -1 for a softer neutrino spectra of E -2.7ν, as indicated by Fermi measurements during the flare. In this paper, we also illustrate the impact of the time-integrated limit on the Crab neutrino steady emission. The limit obtained using 375.5days of the 40-string configuration is compared to existing models of neutrino production from the Crab and its impact on astrophysical parameters is discussed. The most optimistic predictions of some models are already rejected by the IceCube neutrino telescope with more than 90% CL. © 2012 The American Astronomical Society. All rights reserved.