A detection of TeV γ-rays from Mkn 501 is reported, based on observations made between March and August 1996 with the first HEGRA Cherenkov telescope (CT1). From the image analysis, 351 excess candidate γ-ray events are obtained from the 147h dataset. The statistical significance of the excess is 5.2σ. The average excess rate is 2.4+/-0.5h^-1^ above the =~1.5TeV threshold of CT1. Under the assumption that the spectrum of Mkn 501 follows a power law we find a differential spectral index of 2.6+/-0.5 and obtain a time-averaged integral flux above 1.5TeV of 2.3(+/-0.4)_Stat_(+1.5-0.6)_Syst_x10^-12^cm^-2^/s. Comparison with our near contemporary observations of the Crab Nebula, used as a standard candle to test CT1 after upgrading to a 127 pixel camera, indicates that Mkn 501 has a spectrum similar to that of the Crab Nebula above 1.5TeV. The integral flux above 1.5TeV from Mkn 501 is found to have been between 2.2 and 3.6 times smaller than that from the Crab Nebula. HEGRA is the second experiment to have detected Mkn 501 in the TeV range.