diff --git a/ci/deps/actions-37-db.yaml b/ci/deps/actions-37-db.yaml
index edca7b51a3420..8755e1a02c3cf 100644
--- a/ci/deps/actions-37-db.yaml
+++ b/ci/deps/actions-37-db.yaml
@@ -15,7 +15,7 @@ dependencies:
   - beautifulsoup4
   - botocore>=1.11
   - dask
-  - fastparquet>=0.4.0, <=0.5.0
+  - fastparquet>=0.4.0
   - fsspec>=0.7.4
   - gcsfs>=0.6.0
   - geopandas
diff --git a/ci/deps/azure-windows-38.yaml b/ci/deps/azure-windows-38.yaml
index fdea34d573340..661d8813d32d2 100644
--- a/ci/deps/azure-windows-38.yaml
+++ b/ci/deps/azure-windows-38.yaml
@@ -15,7 +15,7 @@ dependencies:
   # pandas dependencies
   - blosc
   - bottleneck
-  - fastparquet>=0.4.0, <=0.5.0
+  - fastparquet>=0.4.0
   - flask
   - fsspec>=0.8.0
   - matplotlib=3.1.3
diff --git a/environment.yml b/environment.yml
index 30fa7c0dea696..2e0228a15272e 100644
--- a/environment.yml
+++ b/environment.yml
@@ -99,7 +99,7 @@ dependencies:
   - xlwt
   - odfpy
 
-  - fastparquet>=0.3.2, <=0.5.0  # pandas.read_parquet, DataFrame.to_parquet
+  - fastparquet>=0.3.2  # pandas.read_parquet, DataFrame.to_parquet
   - pyarrow>=0.15.0  # pandas.read_parquet, DataFrame.to_parquet, pandas.read_feather, DataFrame.to_feather
   - python-snappy  # required by pyarrow
 
diff --git a/pandas/io/parquet.py b/pandas/io/parquet.py
index 5ad014a334c27..34d5edee06791 100644
--- a/pandas/io/parquet.py
+++ b/pandas/io/parquet.py
@@ -327,9 +327,14 @@ def read(
         if is_fsspec_url(path):
             fsspec = import_optional_dependency("fsspec")
 
-            parquet_kwargs["open_with"] = lambda path, _: fsspec.open(
-                path, "rb", **(storage_options or {})
-            ).open()
+            if Version(self.api.__version__) > Version("0.6.1"):
+                parquet_kwargs["fs"] = fsspec.open(
+                    path, "rb", **(storage_options or {})
+                ).fs
+            else:
+                parquet_kwargs["open_with"] = lambda path, _: fsspec.open(
+                    path, "rb", **(storage_options or {})
+                ).open()
         elif isinstance(path, str) and not os.path.isdir(path):
             # use get_handle only when we are very certain that it is not a directory
             # fsspec resources can also point to directories
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 3e421c7715566..ea7ca43742934 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -64,7 +64,7 @@ xlrd
 xlsxwriter
 xlwt
 odfpy
-fastparquet>=0.3.2, <=0.5.0
+fastparquet>=0.3.2
 pyarrow>=0.15.0
 python-snappy
 pyqt5>=5.9.2