We experimentally demonstrate meta-learning-enabled accurate optical signal-to-noise ratio (OSNR) monitoring of directly detected 16QAM signals with extremely few training data. When one-shot training, where one amplitude histogram (AH) for each OSNR value includes only 2000 data samples, is implemented for a 16QAM signal within a variable OSNR range of 15-24 dB, the experimental root mean squared error (RMSE) of the retraining technique is 1.53 dB. For transfer learning from the 16QAM simulation to the experimentally generated AH, the RMSE can be reduced to 1.11 dB. In comparison with both the retraining and transfer learning techniques, the RMSE of meta-learning-enabled OSNR monitoring can be further reduced by 42.8% and 22.3%, respectively. In order to reach the optimal accuracy with an RMSE of 0.66 dB, the meta-learning technique requires only 15 AHs for each OSNR value to be monitored, while the retraining and the transfer learning techniques need 20 and 25 AHs, respectively.