diff --git a/qiskit/result/utils.py b/qiskit/result/utils.py
index 9ed04c139a40..0ff6cd7e5f4f 100644
--- a/qiskit/result/utils.py
+++ b/qiskit/result/utils.py
@@ -80,7 +80,7 @@ def marginal_counts(
                     )  # same convention as for the counts
                     bit_strings = [_hex_to_bin(s) for s in experiment_result.data.memory]
                     marginal_bit_strings = [
-                        "".join([s[-idx - 1] for idx in sorted_indices if idx < len(s)])
+                        "".join([s[-idx - 1] for idx in sorted_indices if idx < len(s)]) or "0"
                         for s in bit_strings
                     ]
                     experiment_result.data.memory = [_bin_to_hex(s) for s in marginal_bit_strings]
diff --git a/releasenotes/notes/fix-marginal_counts-zero-memory-0f6710d6923c8ad7.yaml b/releasenotes/notes/fix-marginal_counts-zero-memory-0f6710d6923c8ad7.yaml
new file mode 100644
index 000000000000..cc2154bce675
--- /dev/null
+++ b/releasenotes/notes/fix-marginal_counts-zero-memory-0f6710d6923c8ad7.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    :func:`.marginal_counts` will now succeed when asked to marginalise memory
+    with an ``indices`` parameter containing non-zero elements.  Previously,
+    shots whose hexadecimal result representation was sufficiently small could
+    raise a ``ValueError``.  See `#8044 <https://github.com/Qiskit/qiskit-terra/issues/8044>`__.
diff --git a/test/python/result/test_result.py b/test/python/result/test_result.py
index 3127e77b30ca..192277a70587 100644
--- a/test/python/result/test_result.py
+++ b/test/python/result/test_result.py
@@ -222,6 +222,16 @@ def test_marginal_counts_result_memory(self):
         marginal_memory = marginal_result.results[0].data.memory
         self.assertEqual(marginal_memory, [hex(ii % 2) for ii in range(8)])
 
+    def test_marginal_counts_result_memory_nonzero_indices(self):
+        """Test that a Result object containing memory marginalizes correctly."""
+        result = self.generate_qiskit_result()
+        index = 2
+        marginal_result = marginal_counts(result, indices=[index])
+        marginal_memory = marginal_result.results[0].data.memory
+        mask = 1 << index
+        expected = [hex((ii & mask) >> index) for ii in range(8)]
+        self.assertEqual(marginal_memory, expected)
+
     def test_marginal_counts_result_memory_indices_None(self):
         """Test that a Result object containing memory marginalizes correctly."""
         result = self.generate_qiskit_result()