diff --git a/cpp/src/arrow/csv/parser.cc b/cpp/src/arrow/csv/parser.cc
index e83855336d2d..54dc54ae7e82 100644
--- a/cpp/src/arrow/csv/parser.cc
+++ b/cpp/src/arrow/csv/parser.cc
@@ -204,7 +204,8 @@ class PresizedValueDescWriter : public ValueDescWriter<PresizedValueDescWriter>
   // however we allow for one extraneous write in case of excessive columns,
   // hence `2 + num_rows * num_cols` (see explanation in PushValue below).
   PresizedValueDescWriter(MemoryPool* pool, int32_t num_rows, int32_t num_cols)
-      : ValueDescWriter(pool, /*values_capacity=*/2 + num_rows * num_cols) {}
+      : ValueDescWriter(
+            pool, /*values_capacity=*/2 + static_cast<int64_t>(num_rows) * num_cols) {}
 
   void PushValue(ParsedValueDesc v) {
     DCHECK_LT(values_size_, values_capacity_);
@@ -535,8 +536,8 @@ class BlockParserImpl {
       // Use bulk filter only if average value length is >= 10 bytes,
       // as the bulk filter has a fixed cost that isn't compensated
       // when values are too short.
-      const int64_t bulk_filter_threshold =
-          batch_.num_cols_ * (batch_.num_rows_ - start_num_rows) * 10;
+      const int64_t bulk_filter_threshold = static_cast<int64_t>(batch_.num_cols_) *
+                                            (batch_.num_rows_ - start_num_rows) * 10;
       use_bulk_filter_ = (data - *out_data) > bulk_filter_threshold;
     }
 
@@ -604,6 +605,17 @@ class BlockParserImpl {
           rows_in_chunk = std::min(kTargetChunkSize, max_num_rows_ - batch_.num_rows_);
         }
 
+        // The values array holds one ParsedValueDesc per cell and those offsets
+        // are 31-bit, so the number of values in a chunk must fit in an int32.
+        // A first line with millions of fields can drive `num_cols_` high enough
+        // to overflow that, so error out rather than presize past the limit.
+        if (static_cast<int64_t>(rows_in_chunk) * batch_.num_cols_ >
+            std::numeric_limits<int32_t>::max()) {
+          return Status::Invalid("CSV parser: row group of ", rows_in_chunk, " rows x ",
+                                 batch_.num_cols_,
+                                 " columns exceeds the maximum number of values");
+        }
+
         ARROW_ASSIGN_OR_RAISE(
             auto values_writer,
             PresizedValueDescWriter::Make(pool_, rows_in_chunk, batch_.num_cols_));
diff --git a/cpp/src/arrow/csv/parser_test.cc b/cpp/src/arrow/csv/parser_test.cc
index 0b5e7175093f..abe57dd2e89c 100644
--- a/cpp/src/arrow/csv/parser_test.cc
+++ b/cpp/src/arrow/csv/parser_test.cc
@@ -666,6 +666,17 @@ TEST(BlockParser, MismatchingNumColumns) {
   }
 }
 
+TEST(BlockParser, TooManyValues) {
+  // A first line carrying millions of fields drives num_cols high enough that
+  // the per-chunk value count (rows x columns) would overflow the 31-bit value
+  // offset, so the parser errors out instead of overflowing.
+  uint32_t out_size;
+  BlockParser parser(ParseOptions::Defaults(), /*num_cols=*/5000000);
+  Status st = Parse(parser, MakeCSVData({"a,b\n"}), &out_size);
+  EXPECT_RAISES_WITH_MESSAGE_THAT(
+      Invalid, testing::HasSubstr("exceeds the maximum number of values"), st);
+}
+
 TEST(BlockParser, MismatchingNumColumnsHandler) {
   struct CustomHandler {
     operator InvalidRowHandler() {