This paper presents a novel algorithm for automatic detection of Glottal Closure Instants (GCI) from the speech signal. Our approach is based on a novel multiscale method that relies on precise estimation of a multiscale parameter at each time instant in the signal domain. This parameter quantifies the degree of signal singularity at each sample from a multi-scale point of view and thus its value can be used to classify signal samples accordingly. We use this property to develop a simple algorithm for detection of GCIs and we show that for the case of clean speech, our algorithm performs almost as well as a recent state-of-the-art method. Next, by performing a comprehensive comparison in presence of 14 different types of noises, we show that our method is more accurate (particularly for very low SNRs). Our method has lower computational times compared to others and does not rely on an estimate of pitch period or any critical choice of parameters.