diff --git a/CHANGES b/CHANGES
index afdd8d436..68b6b1b19 100644
--- a/CHANGES
+++ b/CHANGES
@@ -52,6 +52,8 @@ Bugs fixed
 * #6712: Allow not to install sphinx.testing as runtime (mainly for ALT Linux)
 * #6741: html: search result was broken with empty :confval:`html_file_suffix`
 * #6001: LaTeX does not wrap long code lines at backslash character
+* #6804: LaTeX: PDF build breaks if admonition of danger type contains
+  code-block long enough not to fit on one page
 
 Testing
 --------
diff --git a/sphinx/texinputs/sphinx.sty b/sphinx/texinputs/sphinx.sty
index 6023e6d22..2ae4f5e1c 100644
--- a/sphinx/texinputs/sphinx.sty
+++ b/sphinx/texinputs/sphinx.sty
@@ -1111,6 +1111,9 @@
 \newcommand*\sphinxVerbatimTitle {}
 % This box to typeset the caption before framed.sty multiple passes for framing.
 \newbox\sphinxVerbatim@TitleBox
+% This box to measure contents if nested as inner \MakeFramed requires then
+% minipage encapsulation but too long contents then break outer \MakeFramed
+\newbox\sphinxVerbatim@ContentsBox
 % This is a workaround to a "feature" of French lists, when literal block
 % follows immediately; usable generally (does only \par then), a priori...
 \newcommand*\sphinxvspacefixafterfrenchlists{%
@@ -1257,17 +1260,23 @@
   \itemsep   \z@skip
   \topsep    \z@skip
   \partopsep \z@skip
-  % trivlist will set \parsep to \parskip = zero
+  % trivlist will set \parsep to \parskip (which itself is set to zero above)
   % \leftmargin will be set to zero by trivlist
   \rightmargin\z@
   \parindent  \z@% becomes \itemindent. Default zero, but perhaps overwritten.
   \trivlist\item\relax
-     \ifsphinxverbatimwithminipage\spx@inframedtrue\fi
-     % use a minipage if we are already inside a framed environment
-     \ifspx@inframed\noindent\begin{minipage}{\linewidth}\fi
-     \MakeFramed {% adapted over from framed.sty's snugshade environment
+     \ifspx@inframed\setbox\sphinxVerbatim@ContentsBox\vbox\bgroup
+        \@setminipage\hsize\linewidth
+        % use bulk of minipage paragraph shape restores (this is needed
+        % in indented contexts, at least for some)
+        \textwidth\hsize \columnwidth\hsize \@totalleftmargin\z@
+        \leftskip\z@skip \rightskip\z@skip  \@rightskip\z@skip
+     \else
+       \ifsphinxverbatimwithminipage\noindent\begin{minipage}{\linewidth}\fi
+       \MakeFramed {% adapted over from framed.sty's snugshade environment
         \advance\hsize-\width\@totalleftmargin\z@\linewidth\hsize\@setminipage
         }%
+     \fi
      % For grid placement from \strut's in \FancyVerbFormatLine
      \lineskip\z@skip
      % active comma should not be overwritten by \@noligs
@@ -1279,8 +1288,35 @@
 }
 {%
   \endOriginalVerbatim
-  \par\unskip\@minipagefalse\endMakeFramed % from framed.sty snugshade
-  \ifspx@inframed\end{minipage}\fi
+  \ifspx@inframed
+   \egroup % finish \sphinxVerbatim@ContentsBox vbox
+   \ifdim\dimexpr\ht\sphinxVerbatim@ContentsBox+
+         \dp\sphinxVerbatim@ContentsBox+
+         \ht\sphinxVerbatim@TitleBox+
+         \dp\sphinxVerbatim@TitleBox>.9\textheight
+    % long contents: do not \MakeFramed. Do make a caption (either before or
+    % after) if title exists. Continuation hints across pagebreaks dropped.
+    \spx@opt@verbatimwithframefalse
+    \def\sphinxVerbatim@Title{\noindent\box\sphinxVerbatim@TitleBox\par}%
+    \sphinxVerbatim@Before
+    \noindent\unvbox\sphinxVerbatim@ContentsBox\par
+    \sphinxVerbatim@After
+   \else
+    % short enough contents: use \MakeFramed. As it is nested, this requires
+    % minipage encapsulation. May move to next page as it is non-breakable.
+    \noindent\begin{minipage}{\linewidth}%
+     \MakeFramed {% Use it now with the fetched contents
+      \advance\hsize-\width\@totalleftmargin\z@\linewidth\hsize\@setminipage
+      }%
+     \unvbox\sphinxVerbatim@ContentsBox
+     % some of this may be superfluous:
+     \par\unskip\@minipagefalse\endMakeFramed
+    \end{minipage}%
+   \fi
+  \else % non-nested \MakeFramed
+    \par\unskip\@minipagefalse\endMakeFramed % from framed.sty snugshade
+    \ifsphinxverbatimwithminipage\end{minipage}\fi
+  \fi
   \endtrivlist
 }
 \newenvironment {sphinxVerbatimNoFrame}