The evolution of morphological traits is constrained by the nature and extent of their pleiotropic relationship with other traits. Modularity, where traits with a similar function are pleiotropic whilst pleiotropy is limited between traits belonging to different functions, is thought to enhance evolvability because: (i) modularity reduces the range of effects of deleterious mutations, as mutations would only affect the traits belonging to the targeted module rather than the entire organism, (ii) all traits of a module can respond to natural selection as a unit (iii) it preserves the module’s function during evolutionary change. Despite its key role to explain the evolution of complex organisms, modularity of the genotype-phenotype map has scarcely been directly tested. Here, we adopt an original approach using gene expression traits from 41 mutation accumulation lines as phenotypes, to directly test whether functional modules show enhanced pleiotropy. Using gene expression traits as phenotypes has many advantages that include measuring thousands of traits at the same time and measuring traits that span a large number of functions, easily attributable thanks to several repositories (eg. GO terms and KEGG pathways). Contrary to the prediction of modularity, we found little evidence for higher levels of mutational pleiotropy within functional modules than in random sets of traits. We further compared the strength of selection against mutations that affected traits within functional modules to mutations that affected traits spanning several functions. We found strong selection against traits spanning a very large array of functions. However, against theoretical expectations, we found no evidence for weaker selection on function-specific mutational pleiotropy compared to selection on mutational pleiotropy across functional modules. Together, our results indicate that trait functions do not predict modularity of the genotype-phenotype map, and that mutations targeting a large number of functions are strongly selected against.