diff --git a/datafusion/datasource-parquet/src/opener/mod.rs b/datafusion/datasource-parquet/src/opener/mod.rs
index e188b4543f284..afb1e272aaef1 100644
--- a/datafusion/datasource-parquet/src/opener/mod.rs
+++ b/datafusion/datasource-parquet/src/opener/mod.rs
@@ -1973,6 +1973,20 @@ fn stats_alone_unsatisfiable(
 }
 
 /// Extract constant column values from statistics, keyed by column name in the logical file schema.
+/// Returns true when `data_type` stores IEEE-754 floating point values,
+/// including dictionary encoded floats.
+///
+/// `min == max` does not prove that such a column is constant: parquet writers
+/// exclude `NaN` from `min`/`max` statistics as the format requires, and
+/// `-0.0 == 0.0` compares equal even though the rows differ. Substituting the
+/// statistic for the data would silently rewrite those rows.
+fn is_float_like(data_type: &DataType) -> bool {
+    match data_type {
+        DataType::Dictionary(_, value_type) => value_type.is_floating(),
+        _ => data_type.is_floating(),
+    }
+}
+
 fn constant_columns_from_stats(
     statistics: Option<&Statistics>,
     file_schema: &SchemaRef,
@@ -2014,6 +2028,8 @@ fn constant_value_from_stats(
         && min == max
         && !min.is_null()
         && matches!(column_stats.null_count, Precision::Exact(0))
+        && !is_float_like(&min.data_type())
+        && !is_float_like(data_type)
     {
         // Cast to the expected data type if needed (e.g., Utf8 -> Dictionary)
         if min.data_type() != *data_type {
diff --git a/datafusion/sqllogictest/test_files/parquet_constant_columns.slt b/datafusion/sqllogictest/test_files/parquet_constant_columns.slt
new file mode 100644
index 0000000000000..5b5fa59bad6a0
--- /dev/null
+++ b/datafusion/sqllogictest/test_files/parquet_constant_columns.slt
@@ -0,0 +1,23 @@
+# SPDX-License-Identifier: Apache-2.0
+# SPDX-FileCopyrightText: See the NOTICE file distributed with this work for additional information regarding copyright ownership
+# SPDX-FileContributor: Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements
+
+# Parquet writers exclude NaN from floating point min/max statistics, as the
+# format requires, so a column holding 1.0, NaN and 1.0 has min == max == 1.0
+# and null_count = 0. Statistics must not be used to replace such a projected
+# column with that value: doing so silently turns the NaN row into a 1.0 row.
+statement ok
+COPY (SELECT v::double AS f FROM (VALUES (1.0::double), ('NaN'::double), (1.0::double)) AS t(v))
+TO 'test_files/scratch/parquet_constant_columns/nan.parquet'
+STORED AS PARQUET;
+
+statement ok
+CREATE EXTERNAL TABLE nan_statistics STORED AS PARQUET
+LOCATION 'test_files/scratch/parquet_constant_columns/nan.parquet';
+
+query R
+SELECT f FROM nan_statistics ORDER BY f;
+----
+1
+1
+NaN