diff --git a/docs/changelog/2414.bugfix.rst b/docs/changelog/2414.bugfix.rst
new file mode 100644
index 000000000..118094ea0
--- /dev/null
+++ b/docs/changelog/2414.bugfix.rst
@@ -0,0 +1 @@
+Avoid impossible minversion version requirements. - by :user:`ssbarnea`.
diff --git a/src/tox/provision.py b/src/tox/provision.py
index 95273fe4a..46ca26637 100644
--- a/src/tox/provision.py
+++ b/src/tox/provision.py
@@ -75,6 +75,11 @@ def provision(state: State) -> int | bool:
 
     def add_tox_requires_min_version(requires: list[Requirement]) -> list[Requirement]:
         min_version: Version = state.conf.core["min_version"]
+        # If own version can be a development one or a pre-release, we need to only use its base_version for
+        # requirements, or pip will never be able to find a version that is compatible with the requirement.
+        if min_version.is_devrelease or min_version.is_prerelease:
+            # Earliest possible pre-release number for current base version.
+            min_version = Version(f"{min_version.base_version}a0")
         requires.append(Requirement(f"tox >= {min_version.public}"))
         return requires
 
diff --git a/tests/test_provision.py b/tests/test_provision.py
index 811ac152f..f22d12795 100644
--- a/tests/test_provision.py
+++ b/tests/test_provision.py
@@ -13,6 +13,7 @@
 import pytest
 from filelock import FileLock
 from packaging.requirements import Requirement
+from packaging.version import Version
 
 from tox import __version__
 from tox.pytest import Index, IndexServer, MonkeyPatch, TempPathFactory, ToxProjectCreator
@@ -188,5 +189,6 @@ def test_provision_no_recreate_json(tox_project: ToxProjectCreator) -> None:
     assert msg in result.out
     with (project.path / "out.json").open() as file_handler:
         requires = json.load(file_handler)
-    version = __version__.split("+")[0]
+    # __version__ could be something like 4.0.0rc1.dev1+? so we still need to sanitize it to keep the base and add "a0"
+    version = f"{Version(__version__).base_version}a0"
     assert requires == {"minversion": version, "requires": ["p", f"tox>={version}"]}
diff --git a/whitelist.txt b/whitelist.txt
index 7bd825949..438805295 100644
--- a/whitelist.txt
+++ b/whitelist.txt
@@ -1,8 +1,10 @@
+0rc1
 0x3
 10ms
 1s
 2s
 5s
+a0
 abi
 addinivalue
 addnodes
@@ -48,9 +50,11 @@ dep
 deps
 desc
 dest
+dev1
 devenv
 devnull
 devpi
+devrelease
 dirname
 distinfo
 distlib
@@ -152,6 +156,7 @@ pos
 posargs
 posix
 prepend
+prerelease
 prereleases
 prj
 prog