diff --git a/README.md b/README.md
index 1d51dca352..c72703818e 100644
--- a/README.md
+++ b/README.md
@@ -264,7 +264,7 @@ #### Misc
 <!-- MANPAGE: END EXCLUDED SECTION -->
 
 ## DEPENDENCIES
-Python versions 3.6+ (CPython and PyPy) are supported. Other versions and implementations may or may not work correctly.
+Python versions 3.7+ (CPython and PyPy) are supported. Other versions and implementations may or may not work correctly.
 
 <!-- Python 3.5+ uses VC++14 and it is already embedded in the binary created
 <!x-- https://www.microsoft.com/en-us/download/details.aspx?id=26999 --x>
diff --git a/yt_dlp/YoutubeDL.py b/yt_dlp/YoutubeDL.py
index c595021612..bd6d0d0c1a 100644
--- a/yt_dlp/YoutubeDL.py
+++ b/yt_dlp/YoutubeDL.py
@@ -582,9 +582,14 @@ def __init__(self, params=None, auto_init=True):
             for type_, stream in self._out_files.items_ if type_ != 'console'
         })
 
-        if sys.version_info < (3, 6):
-            self.report_warning(
-                'Python version %d.%d is not supported! Please update to Python 3.6 or above' % sys.version_info[:2])
+        MIN_SUPPORTED, MIN_RECOMMENDED = (3, 6), (3, 7)
+        current_version = sys.version_info[:2]
+        if current_version < MIN_RECOMMENDED:
+            msg = 'Support for Python version %d.%d has been deprecated and will break in future versions of yt-dlp'
+            if current_version < MIN_SUPPORTED:
+                msg = 'Python version %d.%d is no longer supported'
+            self.deprecation_warning(
+                f'{msg}! Please update to Python %d.%d or above' % (*current_version, *MIN_RECOMMENDED))
 
         if self.params.get('allow_unplayable_formats'):
             self.report_warning(