diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 39fe509c6cd29..092515f1e450a 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -46,6 +46,14 @@ repos:
         files: ^(environment.yml|requirements-dev.txt)$
         pass_filenames: false
         additional_dependencies: [pyyaml]
+    -   id: flake8-rst
+        name: flake8-rst
+        description: Run flake8 on code snippets in docstrings or RST files
+        language: python
+        entry: flake8-rst
+        types: [rst]
+        args: [--filename=*.rst]
+        additional_dependencies: [flake8-rst==0.7.0, flake8==3.7.9]
 -   repo: https://github.com/asottile/yesqa
     rev: v1.2.2
     hooks:
diff --git a/ci/code_checks.sh b/ci/code_checks.sh
index b8f6bd53d4a59..784d2c9a411ab 100755
--- a/ci/code_checks.sh
+++ b/ci/code_checks.sh
@@ -73,13 +73,6 @@ if [[ -z "$CHECK" || "$CHECK" == "lint" ]]; then
     flake8 --format="$FLAKE8_FORMAT" pandas/_libs --append-config=flake8/cython-template.cfg
     RET=$(($RET + $?)) ; echo $MSG "DONE"
 
-    echo "flake8-rst --version"
-    flake8-rst --version
-
-    MSG='Linting code-blocks in .rst documentation' ; echo $MSG
-    flake8-rst doc/source --filename=*.rst --format="$FLAKE8_FORMAT"
-    RET=$(($RET + $?)) ; echo $MSG "DONE"
-
     # Check that cython casting is of the form `<type>obj` as opposed to `<type> obj`;
     # it doesn't make a difference, but we want to be internally consistent.
     # Note: this grep pattern is (intended to be) equivalent to the python
diff --git a/environment.yml b/environment.yml
index 6e9b417beb0af..77a9c5fd4822d 100644
--- a/environment.yml
+++ b/environment.yml
@@ -17,9 +17,8 @@ dependencies:
   # code checks
   - black=20.8b1
   - cpplint
-  - flake8<3.8.0  # temporary pin, GH#34150
+  - flake8
   - flake8-comprehensions>=3.1.0  # used by flake8, linting of unnecessary comprehensions
-  - flake8-rst>=0.6.0,<=0.7.0  # linting of code blocks in rst files
   - isort>=5.2.1  # check that imports are in the right order
   - mypy=0.782
   - pre-commit
@@ -113,4 +112,3 @@ dependencies:
   - pip:
     - git+https://github.com/pandas-dev/pydata-sphinx-theme.git@master
     - git+https://github.com/numpy/numpydoc
-    - pyflakes>=2.2.0
diff --git a/requirements-dev.txt b/requirements-dev.txt
index e6346e6c38694..17ca6b8401501 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -8,9 +8,8 @@ asv
 cython>=0.29.21
 black==20.8b1
 cpplint
-flake8<3.8.0
+flake8
 flake8-comprehensions>=3.1.0
-flake8-rst>=0.6.0,<=0.7.0
 isort>=5.2.1
 mypy==0.782
 pre-commit
@@ -79,4 +78,3 @@ tabulate>=0.8.3
 natsort
 git+https://github.com/pandas-dev/pydata-sphinx-theme.git@master
 git+https://github.com/numpy/numpydoc
-pyflakes>=2.2.0