A major part of the human Y chromosome consists of palindromes with multiple copies of genes primarily expressed in testis, many of which have been claimed to affect male fertility. Here we examine copy number variation in these palindromes based on whole genome sequence data from 11,527 Icelandic men. Using a subset of 7947 men grouped into 1449 patrilineal genealogies, we infer 57 large scale de novo copy number mutations affecting palindrome 1. This corresponds to a mutation rate of 2.34 × 10−3mutations per meiosis, which is 4.1 times larger than our phylogenetic estimate of the mutation rate (5.72 × 10−4), suggesting that de novo mutations on the Y are lost faster than expected under neutral evolution. Although simulations indicate a selection coefficient of 1.8% against non-reference copy number carriers, we do not observe differences in fertility among sequenced men associated with their copy number genotype, but we lack statistical power to detect differences resulting from weak negative selection. We also perform association testing of a diverse set of 341 traits to palindromic copy number without any significant associations. We conclude that large-scale palindrome copy number variation on the Y chromosome has little impact on human phenotype diversity.