Answer selection in open-domain dialogues aims to select an accurate answer from candidates. The recent success of answer selection models hinges on training with large amounts of labeled data. However, collecting large-scale labeled data is labor-intensive and time-consuming. In this paper, we introduce the predicted intent labels to calibrate answer labels in a self-training paradigm. Specifically, we propose intent-calibrated self-training (ICAST) to improve the quality of pseudo answer labels through the intent-calibrated answer selection paradigm, in which we employ pseudo intent labels to help improve pseudo answer labels. We carry out extensive experiments on two benchmark datasets with open-domain dialogues. The experimental results show that ICAST outperforms baselines consistently with 1%, 5%, and 10% labeled data. Specifically, it improves 2.06% and 1.00% of F1 score on the two datasets, compared with the strongest baseline with only 5% labeled data.