diff --git a/constraints.txt b/constraints.txt
index 455610b304cf..07b9862e426c 100644
--- a/constraints.txt
+++ b/constraints.txt
@@ -11,3 +11,8 @@ numpy<1.25
 # eigensystem code for one of the test cases.  See
 # https://github.com/Qiskit/qiskit-terra/issues/10345 for current details.
 scipy<1.11
+
+# Aer 0.13 causes several randomised tests to begin failing, and some
+# `QuantumInstance` use of noise models to raise exceptions.  These need fixes
+# on Terra.
+qiskit-aer==0.12.2