Skeletal dysplasias collectively affect a large number of patients worldwide. The majority of these disorders cause growth anomalies. Hence, assessing skeletal maturity via determining the bone age (BA) is one of the most valuable tools for their diagnoses. Moreover, consecutive BA assessments are crucial for monitoring the pediatric growth of patients with such disorders, especially for timing hormone treatments or orthopedic interventions. However, manual BA assessment is time-consuming and suffers from high intra-and inter-rater variability. This is further exacerbated by genetic disorders causing severe skeletal malformations. While numerous approaches to automatize BA assessment were proposed, few were validated for BA assessment on children with abnormal development. In this work, we present Deeplasia, an open-source prior-free deep-learning ensemble approach. After training on the public RSNA BA dataset, we achieve state-of-the-art performance with a mean absolute difference (MAD) of 3.87 months based on the average of six different reference ratings. Next, we demonstrate that Deeplasia generalizes to an unseen dataset of 568 X-ray images from 189 patients with molecularly confirmed diagnoses of seven different genetic bone disorders (including Achondroplasia and Hypochondroplasia) achieving a MAD of 5.84 months w.r.t. to the average of two references. Further, using longitudinal data from a subset of the cohort (149 images), we estimate the test-retest precision of our model ensemble to be at least at the human expert level (2.74 months). We conclude that Deeplasia suits assessing and monitoring the BA in patients with skeletal dysplasias.