diff --git a/setup.py b/setup.py
index 48f6dfd337..2d1a8df97c 100644
--- a/setup.py
+++ b/setup.py
@@ -179,7 +179,7 @@ def _get_arrow_lib_as_linker_input(self):
         'pycryptodomex>=3.2,!=3.5.0,<4.0.0',
         'pyOpenSSL>=16.2.0,<21.0.0',
         'cffi>=1.9,<1.14',
-        'cryptography>=2.5.0,<3.0.0',
+        'cryptography>=2.5.0,<42.0.0',
         'ijson<3.0.0',
         'pyjwt<2.0.0',
         'idna<2.10',
diff --git a/tested_requirements/requirements_35.txt b/tested_requirements/requirements_35.txt
index db4eb9c839..ac597d81ae 100644
--- a/tested_requirements/requirements_35.txt
+++ b/tested_requirements/requirements_35.txt
@@ -7,7 +7,7 @@ botocore==1.14.17
 certifi==2020.4.5.1
 cffi==1.13.2
 chardet==3.0.4
-cryptography==2.9.2
+cryptography==41.0.3
 docutils==0.15.2
 idna==2.9
 ijson==2.6.1
diff --git a/tested_requirements/requirements_36.txt b/tested_requirements/requirements_36.txt
index c8d08ab969..bd38b299f9 100644
--- a/tested_requirements/requirements_36.txt
+++ b/tested_requirements/requirements_36.txt
@@ -7,7 +7,7 @@ botocore==1.14.17
 certifi==2020.4.5.1
 cffi==1.13.2
 chardet==3.0.4
-cryptography==2.9.2
+cryptography==41.0.3
 docutils==0.15.2
 idna==2.9
 ijson==2.6.1
diff --git a/tested_requirements/requirements_37.txt b/tested_requirements/requirements_37.txt
index 92e4445ee4..aa7a09085d 100644
--- a/tested_requirements/requirements_37.txt
+++ b/tested_requirements/requirements_37.txt
@@ -7,7 +7,7 @@ botocore==1.14.17
 certifi==2020.4.5.1
 cffi==1.13.2
 chardet==3.0.4
-cryptography==2.9.2
+cryptography==41.0.3
 docutils==0.15.2
 idna==2.9
 ijson==2.6.1
diff --git a/tested_requirements/requirements_38.txt b/tested_requirements/requirements_38.txt
index 01df7d0feb..98d73e14c4 100644
--- a/tested_requirements/requirements_38.txt
+++ b/tested_requirements/requirements_38.txt
@@ -7,7 +7,7 @@ botocore==1.14.17
 certifi==2020.4.5.1
 cffi==1.13.2
 chardet==3.0.4
-cryptography==2.9.2
+cryptography==41.0.3
 docutils==0.15.2
 idna==2.9
 ijson==2.6.1