Background: Analysis of tissue biopsy whole-slide images (WSIs) depends on effective detection and elimination of image artifacts. We present a novel method to detect tissue-fold artifacts in histopathological WSIs. We also study the effect of tissue folds on image features and prediction models. Materials and Methods: We use WSIs of samples from two cancer endpoints - kidney clear cell carcinoma (KiCa) and ovarian serous adenocarcinoma (OvCa) - publicly available from The Cancer Genome Atlas. We detect tissue folds in low-resolution WSIs using color properties and two adaptive connectivity-based thresholds. We optimize and validate our tissue-fold detection method using 105 manually annotated WSIs from both cancer endpoints. In addition to detecting tissue folds, we extract 461 image features from the high-resolution WSIs for all samples. We use the rank-sum test to find image features that are statistically different among features extracted from the same set of WSIs with and without folds. We then use features that are affected by tissue folds to develop models for predicting cancer grades. Results: When compared to the ground truth, our method detects tissue folds in KiCa with 0.50 adjusted Rand index (ARI), 0.77 average true rate (ATR), 0.55 true positive rate (TPR), and 0.98 true negative rate (TNR); and in OvCa with 0.40 ARI, 0.73 ATR, 0.47 TPR, and 0.98 TNR. Compared to two other methods, our method is more accurate in terms of ARI and ATR. We found that 53 and 30 image features were significantly affected by the presence of tissue-fold artifacts (detected using our method) in OvCa and KiCa, respectively. After eliminating tissue folds, the performance of cancer-grade prediction models improved by 5% and 1% in OvCa and KiCa, respectively. Conclusion: The proposed connectivity-based method is more effective in detecting tissue folds compared to other methods. Reducing tissue-fold artifacts will increase the performance of cancer-grade prediction models.