In eukaryotes, the three-dimensional (3D) conformation of the genome is far from random, and this nonrandom chromatin organization is strongly correlated with gene expression and protein function, which are two critical determinants of the selective constraints and evolutionary rates of genes. However, whether genes and other elements that are located close to each other in the 3D genome evolve in a coordinated way has not been investigated in any organism. To address this question, we constructed chromatin interaction networks (CINs) in Arabidopsis thaliana based on high-throughput chromosome conformation capture data and demonstrated that adjacent large DNA fragments in the CIN indeed exhibit more similar levels of polymorphism and evolutionary rates than random fragment pairs. Using simulations that account for the linear distance between fragments, we proved that the 3D chromosomal organization plays a role in the observed correlated evolution. Spatially interacting fragments also exhibit more similar mutation rates and functional constraints in both coding and noncoding regions than the random expectations, indicating that the correlated evolution between 3D neighbors is a result of combined evolutionary forces. A collection of 39 genomic and epigenomic features can explain much of the variance in genetic diversity and evolutionary rates across the genome. Moreover, features that have a greater effect on the evolution of regional sequences tend to show higher similarity between neighboring fragments in the CIN, suggesting a pivotal role of epigenetic modifications and chromatin organization in determining the correlated evolution of large DNA fragments in the 3D genome.