Fetal alcohol syndrome (FAS) caused by prenatal alcohol exposure can result in a series of cranio-facial anomalies, and behavioral and neurocognitive problems. Current diagnosis of FAS is typically done by identifying a set of facial characteristics, which are often obtained by manual examination. Anatomical landmark detection, which provides rich geometric information, is important to detect the presence of FAS associated facial anomalies. This imaging application is characterized by large variations in data appearance and limited availability of labeled data. Current deep learning-based heatmap regression methods designed for facial landmark detection in natural images assume availability of large datasets and are therefore not wellsuited for this application. To address this restriction, we develop a new regularized transfer learning approach that exploits the knowledge of a network learned on large facial recognition datasets. In contrast to standard transfer learning which focuses on adjusting the pre-trained weights, the proposed learning approach regularizes the model behavior. It explicitly reuses the rich visual semantics of a domain-similar source model on the target task data as an additional supervisory signal for regularizing landmark detection optimization. Specifically, we develop four regularization constraints for the proposed transfer learning, including constraining the feature outputs from classification and intermediate layers, as well as matching activation attention maps in both spatial and channel levels. Experimental evaluation on a collected clinical imaging dataset demonstrate that the proposed approach can effectively improve model generalizability under limited training samples, and is advantageous to other approaches in the literature.