Purpose: To develop and evaluate a method for rapid estimation of multiparametric T1, T2, proton density (PD), and inversion efficiency (IE) maps from 3D-quantification using an interleaved Look-Locker acquisition sequence with T2 preparation pulse (3D-QALAS) measurements using self-supervised learning (SSL) without the need for an external dictionary. Methods: A SSL-based QALAS mapping method (SSL-QALAS) was developed for rapid and dictionary-free estimation of multiparametric maps from 3D-QALAS measurements. The accuracy of the reconstructed quantitative maps using dictionary matching and SSL-QALAS was evaluated by comparing the estimated T1 and T2 values with those obtained from the reference methods on an ISMRM/NIST phantom. The SSL-QALAS and the dictionary matching methods were also compared in vivo, and generalizability was evaluated by comparing the scan-specific, pre-trained, and transfer learning models. Results: Phantom experiments showed that both the dictionary matching and SSL-QALAS methods produced T1 and T2 estimates that had a strong linear agreement with the reference values in the ISMRM/NIST phantom. Further, SSL-QALAS showed similar performance with dictionary matching in reconstructing the T1, T2, PD, and IE maps on in vivo data. Rapid reconstruction of multiparametric maps was enabled by inferring the data using a pre-trained SSL-QALAS model within 10 s. Fast scan-specific tuning was also demonstrated by fine-tuning the pre-trained model with the target subject's data within 15 min. Conclusion: The proposed SSL-QALAS method enabled rapid reconstruction of multiparametric maps from 3D-QALAS measurements without an external dictionary or labeled ground-truth training data.