diff --git a/changes/1417-vdwees.md b/changes/1417-vdwees.md
new file mode 100644
index 0000000000..4f191031b7
--- /dev/null
+++ b/changes/1417-vdwees.md
@@ -0,0 +1,3 @@
+Modify schema constraints on `ConstrainedFloat` so that `exclusiveMinimum` and
+minimum are not included in the schema if they are equal to `-math.inf` and
+`exclusiveMaximum` and `maximum` are not included if they are equal to `math.inf`.
diff --git a/pydantic/schema.py b/pydantic/schema.py
index 63e2058adf..ec0a085468 100644
--- a/pydantic/schema.py
+++ b/pydantic/schema.py
@@ -234,6 +234,9 @@ def get_field_schema_validations(field: ModelField) -> Dict[str, Any]:
         f_schema['const'] = field.default
     if field.field_info.extra:
         f_schema.update(field.field_info.extra)
+    modify_schema = getattr(field.type_, '__modify_schema__', None)
+    if modify_schema:
+        modify_schema(f_schema)
     return f_schema
 
 
diff --git a/pydantic/types.py b/pydantic/types.py
index 8eb72d6ac9..2b7a64e946 100644
--- a/pydantic/types.py
+++ b/pydantic/types.py
@@ -1,3 +1,4 @@
+import math
 import re
 import warnings
 from decimal import Decimal
@@ -339,6 +340,15 @@ def __modify_schema__(cls, field_schema: Dict[str, Any]) -> None:
             maximum=cls.le,
             multipleOf=cls.multiple_of,
         )
+        # Modify constraints to account for differences between IEEE floats and JSON
+        if field_schema.get('exclusiveMinimum') == -math.inf:
+            del field_schema['exclusiveMinimum']
+        if field_schema.get('minimum') == -math.inf:
+            del field_schema['minimum']
+        if field_schema.get('exclusiveMaximum') == math.inf:
+            del field_schema['exclusiveMaximum']
+        if field_schema.get('maximum') == math.inf:
+            del field_schema['maximum']
 
     @classmethod
     def __get_validators__(cls) -> 'CallableGenerator':
diff --git a/tests/test_schema.py b/tests/test_schema.py
index e78ddb69e0..b0bd2f0206 100644
--- a/tests/test_schema.py
+++ b/tests/test_schema.py
@@ -1,3 +1,4 @@
+import math
 import os
 import sys
 import tempfile
@@ -1119,6 +1120,10 @@ class UserModel(BaseModel):
         ({'lt': 5}, float, {'type': 'number', 'exclusiveMaximum': 5}),
         ({'ge': 2}, float, {'type': 'number', 'minimum': 2}),
         ({'le': 5}, float, {'type': 'number', 'maximum': 5}),
+        ({'gt': -math.inf}, float, {'type': 'number'}),
+        ({'lt': math.inf}, float, {'type': 'number'}),
+        ({'ge': -math.inf}, float, {'type': 'number'}),
+        ({'le': math.inf}, float, {'type': 'number'}),
         ({'multiple_of': 5}, float, {'type': 'number', 'multipleOf': 5}),
         ({'gt': 2}, Decimal, {'type': 'number', 'exclusiveMinimum': 2}),
         ({'lt': 5}, Decimal, {'type': 'number', 'exclusiveMaximum': 5}),