diff --git a/metrics/bertscore/README.md b/metrics/bertscore/README.md
index af8a5356f..25f736f51 100644
--- a/metrics/bertscore/README.md
+++ b/metrics/bertscore/README.md
@@ -61,6 +61,8 @@ BERTScore also accepts multiple optional arguments:
 
 `use_fast_tokenizer` (bool): `use_fast` parameter passed to HF tokenizer. The default value is `False`. 
 
+`max_length` (int): Number of tokens the inputs are truncated to. Defaults to the `model_max_length` of the model's tokenizer, or to 512 when the tokenizer does not define one.
+
 
 ## Output values
 
diff --git a/metrics/bertscore/bertscore.py b/metrics/bertscore/bertscore.py
index 071e76ff3..788675b8d 100644
--- a/metrics/bertscore/bertscore.py
+++ b/metrics/bertscore/bertscore.py
@@ -14,6 +14,7 @@
 """ BERTScore metric. """
 
 import functools
+import sys
 from contextlib import contextmanager
 
 import bert_score
@@ -23,6 +24,31 @@
 import evaluate
 
 
+logger = evaluate.logging.get_logger(__name__)
+
+# Fallback truncation length for tokenizers that don't declare `model_max_length`. 512 is the
+# sequence length of the BERT-family models `bert_score` recommends for each language.
+_DEFAULT_MODEL_MAX_LENGTH = 512
+
+
+def _set_tokenizer_max_length(tokenizer, max_length=None):
+    """Make sure the tokenizer reports a truncation length the tokenizers backend can represent.
+
+    Tokenizers whose config omits `model_max_length` report transformers' `VERY_LARGE_INTEGER`
+    sentinel (~1e30) instead. `bert_score` forwards that value to `tokenizer.encode(max_length=...)`,
+    which raises `OverflowError` in the Rust tokenizers backend used by transformers>=5.
+    """
+    if max_length is None:
+        if tokenizer.model_max_length <= sys.maxsize:
+            return
+        max_length = _DEFAULT_MODEL_MAX_LENGTH
+        logger.warning(
+            f"The tokenizer does not define `model_max_length`, truncating inputs to {max_length} tokens. "
+            "Pass `max_length` to `compute()` to use a different length."
+        )
+    tokenizer.model_max_length = max_length
+
+
 @contextmanager
 def filter_logging_context():
     def filter_log(record):
@@ -79,6 +105,9 @@ def filter_log(record):
     rescale_with_baseline (bool): Rescale bertscore with pre-computed baseline.
     baseline_path (str): Customized baseline file.
     use_fast_tokenizer (bool): `use_fast` parameter passed to HF tokenizer. New in version 0.3.10.
+    max_length (int): Number of tokens the inputs are truncated to. Defaults to the
+        `model_max_length` of the model's tokenizer, or to 512 when the tokenizer does not
+        define one.
 
 Returns:
     precision: Precision.
@@ -142,6 +171,7 @@ def _compute(
         rescale_with_baseline=False,
         baseline_path=None,
         use_fast_tokenizer=False,
+        max_length=None,
     ):
 
         if isinstance(references[0], str):
@@ -185,7 +215,10 @@ def _compute(
         )
 
         with filter_logging_context():
-            if not hasattr(self, "cached_bertscorer") or self.cached_bertscorer.hash != hashcode:
+            is_new_scorer = not hasattr(self, "cached_bertscorer") or self.cached_bertscorer.hash != hashcode
+            if is_new_scorer:
+                # `idf_sents` are tokenized below instead of by the scorer itself, so that the
+                # truncation length is fixed up first.
                 self.cached_bertscorer = scorer(
                     model_type=model_type,
                     num_layers=num_layers,
@@ -193,13 +226,18 @@ def _compute(
                     nthreads=nthreads,
                     all_layers=all_layers,
                     idf=idf,
-                    idf_sents=idf_sents,
+                    idf_sents=None,
                     device=device,
                     lang=lang,
                     rescale_with_baseline=rescale_with_baseline,
                     baseline_path=baseline_path,
                 )
 
+            _set_tokenizer_max_length(self.cached_bertscorer._tokenizer, max_length)
+
+            if is_new_scorer and idf_sents is not None:
+                self.cached_bertscorer.compute_idf(idf_sents)
+
         (P, R, F) = self.cached_bertscorer.score(
             cands=predictions,
             refs=references,
diff --git a/tests/test_metric_common.py b/tests/test_metric_common.py
index 014dc0b32..a05bb0c7b 100644
--- a/tests/test_metric_common.py
+++ b/tests/test_metric_common.py
@@ -219,6 +219,37 @@ def predict(self, data, *args, **kwargs):
             yield
 
 
+def _load_bertscore_with_tokenizer(model_max_length):
+    from transformers import AutoTokenizer
+
+    tokenizer = AutoTokenizer.from_pretrained("hf-internal-testing/tiny-random-bert")
+    tokenizer.model_max_length = model_max_length
+    return load(os.path.join("metrics", "bertscore")), tokenizer
+
+
+def test_bertscore_caps_undefined_model_max_length():
+    # regression test for https://github.com/huggingface/evaluate/issues/739: tokenizers without a
+    # `model_max_length` report a sentinel value that overflows the Rust tokenizers backend
+    from transformers.tokenization_utils_base import VERY_LARGE_INTEGER
+
+    metric, tokenizer = _load_bertscore_with_tokenizer(VERY_LARGE_INTEGER)
+    with patch_bertscore("bertscore"), patch("bert_score.scorer.get_tokenizer", return_value=tokenizer):
+        results = metric.compute(
+            predictions=["hello there"], references=["hello there"], lang="en", idf=True, nthreads=0
+        )
+
+    assert tokenizer.model_max_length == 512
+    assert results["f1"] == [1.0]
+
+
+def test_bertscore_max_length_overrides_model_max_length():
+    metric, tokenizer = _load_bertscore_with_tokenizer(512)
+    with patch_bertscore("bertscore"), patch("bert_score.scorer.get_tokenizer", return_value=tokenizer):
+        metric.compute(predictions=["hello there"], references=["hello there"], lang="en", max_length=128)
+
+    assert tokenizer.model_max_length == 128
+
+
 def test_seqeval_raises_when_incorrect_scheme():
     metric = load(os.path.join("metrics", "seqeval"))
     wrong_scheme = "ERROR"