diff --git a/changelog/68775.fixed.md b/changelog/68775.fixed.md
new file mode 100644
index 000000000000..fbd29bee257e
--- /dev/null
+++ b/changelog/68775.fixed.md
@@ -0,0 +1 @@
+Remove the integer-to-string conversion limit for `test.fib` function.
diff --git a/salt/modules/test.py b/salt/modules/test.py
index 3cd9d7d5ea43..2c5a236e1747 100644
--- a/salt/modules/test.py
+++ b/salt/modules/test.py
@@ -346,6 +346,12 @@ def fib(num):
 
         salt '*' test.fib 3
     """
+    # Remove the limit on the number of digits in an int,
+    # as Fibonacci numbers grow very quickly.
+    # The default limit for integer string conversion is 4300 digits,
+    # which means that num > 20577 will fail with a ValueError.
+    sys.set_int_max_str_digits(0)
+
     num = int(num)
     if num < 0:
         raise ValueError("Negative number is not allowed!")
diff --git a/tests/pytests/integration/cli/test_salt_call.py b/tests/pytests/integration/cli/test_salt_call.py
index f927f499c858..5df8b87be1ad 100644
--- a/tests/pytests/integration/cli/test_salt_call.py
+++ b/tests/pytests/integration/cli/test_salt_call.py
@@ -34,6 +34,11 @@ def test_fib(salt_call_cli):
     assert ret.data[0] == 2
 
 
+def test_fib_str_limit(salt_call_cli):
+    ret = salt_call_cli.run("test.fib", "20578")
+    assert ret.returncode == 0
+
+
 def test_fib_txt_output(salt_call_cli):
     ret = salt_call_cli.run("--output=txt", "test.fib", "3")
     assert ret.returncode == 0