Convolution neural networks (CNNs) have shown great success in various applications. However, the computational complexity and memory storage of CNNs is a bottleneck for their deployment on resource-constrained devices. Recent efforts towards reducing the computation cost and the memory overhead of CNNs involve similarity-based passive filter pruning methods. Similarity-based passive filter pruning methods compute a pairwise similarity matrix for the filters and eliminate a few similar filters to obtain a small pruned CNN. However, the computational complexity of computing the pairwise similarity matrix is high, particularly when a convolutional layer has many filters. To reduce the computational complexity in obtaining the pairwise similarity matrix, we propose to use an efficient method where the complete pairwise similarity matrix is approximated from only a few of its columns by using a Nyström approximation method. The proposed efficient similarity-based passive filter pruning method is 3 times faster and gives same accuracy at the same reduction in computations for CNNs compared to that of the similarity-based pruning method that computes a complete pairwise similarity matrix. Apart from this, the proposed efficient similarity-based pruning method performs similarly or better than the existing norm-based pruning methods. The efficacy of the proposed pruning method is evaluated on CNNs such as DCASE 2021 Task 1A baseline network and a VGGish network designed for acoustic scene classification.