Poor Precision-Recall curve for binary classifier trained on balanced data, with imbalanced test data
The precision-recall curve and the ROC curve respond very differently to class imbalance. The precision-recall curve is very sensitive to imbalance while the ROC curve can mask the effect of imbalance. 

For the TPR (=recall) and FPR you divide by the true number of samples in each class, while for precision you divide by the number of positive predictions. 

If you have few positive samples the ratio between false and true positives becomes more sensitive (compared to false positives [few] and all true negatives [many]).

Depending on your use case, this might be a problem (or not) and should be part of your evaluation.