diff --git a/qiskit/circuit/quantumcircuit.py b/qiskit/circuit/quantumcircuit.py
index 84ec38fd20c..0acda794b1b 100644
--- a/qiskit/circuit/quantumcircuit.py
+++ b/qiskit/circuit/quantumcircuit.py
@@ -1250,10 +1250,21 @@ def add_register(self, *regs: Union[Register, int, Sequence[Bit]]) -> None:
             # QuantumCircuit defined without registers
             if len(regs) == 1 and isinstance(regs[0], int):
                 # QuantumCircuit with anonymous quantum wires e.g. QuantumCircuit(2)
-                regs = (QuantumRegister(regs[0], "q"),)
+                if regs[0] == 0:
+                    regs = tuple()
+                else:
+                    regs = (QuantumRegister(regs[0], "q"),)
             elif len(regs) == 2 and all(isinstance(reg, int) for reg in regs):
                 # QuantumCircuit with anonymous wires e.g. QuantumCircuit(2, 3)
-                regs = (QuantumRegister(regs[0], "q"), ClassicalRegister(regs[1], "c"))
+                if regs[0] == 0:
+                    qregs = tuple()
+                else:
+                    qregs = (QuantumRegister(regs[0], "q"),)
+                if regs[1] == 0:
+                    cregs = tuple()
+                else:
+                    cregs = (ClassicalRegister(regs[1], "c"),)
+                regs = qregs + cregs
             else:
                 raise CircuitError(
                     "QuantumCircuit parameters can be Registers or Integers."
diff --git a/qiskit/circuit/register.py b/qiskit/circuit/register.py
index 9ee42852e7c..b6bf92188fd 100644
--- a/qiskit/circuit/register.py
+++ b/qiskit/circuit/register.py
@@ -82,9 +82,9 @@ def __init__(self, size=None, name=None, bits=None):
             )
         size = int(size)  # cast to int
 
-        if size <= 0:
+        if size < 0:
             raise CircuitError(
-                "Register size must be positive (%s '%s' was provided)"
+                "Register size must be non-negative (%s '%s' was provided)"
                 % (type(size).__name__, size)
             )
 
diff --git a/test/python/circuit/test_circuit_registers.py b/test/python/circuit/test_circuit_registers.py
index cad43a7b150..1ae3cdda0f5 100644
--- a/test/python/circuit/test_circuit_registers.py
+++ b/test/python/circuit/test_circuit_registers.py
@@ -148,6 +148,18 @@ def test_qubits(self):
         self.assertEqual(qubits[1], qr2[1])
         self.assertEqual(qubits[2], qr1[0])
 
+    def test_circuit_without_classical_register(self):
+        """Test QuantumCircuit constructor."""
+        qc = QuantumCircuit(2, 0)
+        self.assertEqual(qc.cregs, [])
+
+    def test_circuit_without_quantum_register(self):
+        """Test QuantumCircuit constructor."""
+        qc = QuantumCircuit(0, 3)
+        self.assertEqual(qc.qregs, [])
+        self.assertEqual(len(qc.cregs), 1)
+        self.assertEqual(qc.cregs[0].size, 3)
+
     def test_clbits(self):
         """Test clbits() method."""
         qr1 = QuantumRegister(1, "q1")
diff --git a/test/python/circuit/test_register.py b/test/python/circuit/test_register.py
index 96ca5e6ea73..ea45f03a08d 100644
--- a/test/python/circuit/test_register.py
+++ b/test/python/circuit/test_register.py
@@ -51,6 +51,16 @@ def test_init_raise_if_passed_invalid_name(self, reg_type):
         with self.assertRaisesRegex(CircuitError, "invalid OPENQASM register name"):
             _ = reg_type(size=1, name="_q")
 
+    @data(QuantumRegister, ClassicalRegister, AncillaRegister)
+    def test_init_with_zero_size(self, reg_type):
+        register = reg_type(0)
+        self.assertEqual(register.size, 0)
+
+    @data(QuantumRegister, ClassicalRegister, AncillaRegister)
+    def test_init_raise_if_negative_size(self, reg_type):
+        with self.assertRaisesRegex(CircuitError, "Register size must be non-negative"):
+            _ = reg_type(-1)
+
     @data(QuantumRegister, ClassicalRegister, AncillaRegister)
     def test_implicit_bit_construction_from_size(self, reg_type):
         reg = reg_type(2)