In this paper, we will show that Approximate Entropy (ApEn) can be used to detect high-quality speech frames in an otherwise distorted speech signal. By exploiting the property of quasi-periodicity in speech, ApEn is able to detect small aberrations in speech frames that would otherwise cause a decrease in the performance in an automatic speaker recognition (ASR) system. In addition, we obtain the statistics of ApEn values representative of clean speech and propose threshold bounds to obtain maximum recognition rates. When compared to other popular voice activity detector (VAD) algorithms, our simulation results showed that utilization of ApEn will outperform the other VADs in discerning clean speech from noisy speech. This ability to properly detect clean speech allows for a speaker recognition system to obtain a recognition rate close to 87%, which is close to the same performance of the system when noise is not present.