diff --git a/qiskit/primitives/backend_estimator.py b/qiskit/primitives/backend_estimator.py
index 0e48c5080b45..40c77f9e9a6b 100644
--- a/qiskit/primitives/backend_estimator.py
+++ b/qiskit/primitives/backend_estimator.py
@@ -16,6 +16,7 @@
 from __future__ import annotations
 
 import copy
+import typing
 from collections.abc import Sequence
 from itertools import accumulate
 
@@ -23,7 +24,6 @@
 
 from qiskit.circuit import QuantumCircuit
 from qiskit.compiler import transpile
-from qiskit.opflow import PauliSumOp
 from qiskit.providers import BackendV1, BackendV2, Options
 from qiskit.quantum_info import Pauli, PauliList
 from qiskit.quantum_info.operators.base_operator import BaseOperator
@@ -34,6 +34,9 @@
 from .primitive_job import PrimitiveJob
 from .utils import _circuit_key, _observable_key, init_observable
 
+if typing.TYPE_CHECKING:
+    from qiskit.opflow import PauliSumOp
+
 
 def _run_circuits(
     circuits: QuantumCircuit | list[QuantumCircuit],
diff --git a/qiskit/primitives/base/base_estimator.py b/qiskit/primitives/base/base_estimator.py
index f091bc0d335c..1dec010d7b12 100644
--- a/qiskit/primitives/base/base_estimator.py
+++ b/qiskit/primitives/base/base_estimator.py
@@ -84,10 +84,10 @@
 from collections.abc import Sequence
 from copy import copy
 from typing import Generic, TypeVar
+import typing
 
 from qiskit.circuit import QuantumCircuit
 from qiskit.circuit.parametertable import ParameterView
-from qiskit.opflow import PauliSumOp
 from qiskit.providers import JobV1 as Job
 from qiskit.quantum_info.operators import SparsePauliOp
 from qiskit.quantum_info.operators.base_operator import BaseOperator
@@ -95,6 +95,9 @@
 from ..utils import init_observable
 from .base_primitive import BasePrimitive
 
+if typing.TYPE_CHECKING:
+    from qiskit.opflow import PauliSumOp
+
 T = TypeVar("T", bound=Job)
 
 
diff --git a/qiskit/primitives/estimator.py b/qiskit/primitives/estimator.py
index 7333e44332c9..8afa7783ee40 100644
--- a/qiskit/primitives/estimator.py
+++ b/qiskit/primitives/estimator.py
@@ -17,12 +17,12 @@
 
 from collections.abc import Sequence
 from typing import Any
+import typing
 
 import numpy as np
 
 from qiskit.circuit import QuantumCircuit
 from qiskit.exceptions import QiskitError
-from qiskit.opflow import PauliSumOp
 from qiskit.quantum_info import Statevector
 from qiskit.quantum_info.operators.base_operator import BaseOperator
 
@@ -35,6 +35,9 @@
     init_observable,
 )
 
+if typing.TYPE_CHECKING:
+    from qiskit.opflow import PauliSumOp
+
 
 class Estimator(BaseEstimator[PrimitiveJob[EstimatorResult]]):
     """
diff --git a/qiskit/primitives/utils.py b/qiskit/primitives/utils.py
index 40165077e291..20db6c0d7295 100644
--- a/qiskit/primitives/utils.py
+++ b/qiskit/primitives/utils.py
@@ -14,6 +14,8 @@
 """
 from __future__ import annotations
 
+import sys
+import typing
 from collections.abc import Iterable
 
 import numpy as np
@@ -21,11 +23,13 @@
 from qiskit.circuit import Instruction, ParameterExpression, QuantumCircuit
 from qiskit.circuit.bit import Bit
 from qiskit.extensions.quantum_initializer.initializer import Initialize
-from qiskit.opflow import PauliSumOp
 from qiskit.quantum_info import SparsePauliOp, Statevector
 from qiskit.quantum_info.operators.base_operator import BaseOperator
 from qiskit.quantum_info.operators.symplectic.base_pauli import BasePauli
 
+if typing.TYPE_CHECKING:
+    from qiskit.opflow import PauliSumOp
+
 
 def init_circuit(state: QuantumCircuit | Statevector) -> QuantumCircuit:
     """Initialize state by converting the input to a quantum circuit.
@@ -58,9 +62,18 @@ def init_observable(observable: BaseOperator | PauliSumOp | str) -> SparsePauliO
         TypeError: If the observable is a :class:`~qiskit.opflow.PauliSumOp` and has a parameterized
             coefficient.
     """
+    # This dance is to avoid importing the deprecated `qiskit.opflow` if the user hasn't already
+    # done so.  They can't hold a `qiskit.opflow.PauliSumOp` if `qiskit.opflow` hasn't been
+    # imported, and we don't want unrelated Qiskit library code to be responsible for the first
+    # import, so the deprecation warnings will show.
+    if "qiskit.opflow" in sys.modules:
+        pauli_sum_check = sys.modules["qiskit.opflow"].PauliSumOp
+    else:
+        pauli_sum_check = ()
+
     if isinstance(observable, SparsePauliOp):
         return observable
-    elif isinstance(observable, PauliSumOp):
+    elif isinstance(observable, pauli_sum_check):
         if isinstance(observable.coeff, ParameterExpression):
             raise TypeError(
                 f"Observable must have numerical coefficient, not {type(observable.coeff)}."
diff --git a/releasenotes/notes/fix-primitives-import-warnings-439e3e237fdb9d7b.yaml b/releasenotes/notes/fix-primitives-import-warnings-439e3e237fdb9d7b.yaml
new file mode 100644
index 000000000000..f3827cca160c
--- /dev/null
+++ b/releasenotes/notes/fix-primitives-import-warnings-439e3e237fdb9d7b.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Importing :mod:`qiskit.primitives` will no longer cause deprecation warnings stemming from the
+    deprecated :mod:`qiskit.opflow` module.  These warnings would have been hidden to users by the
+    default Python filters, but triggered the eager import of :mod:`.opflow`, which meant that a
+    subsequent import by a user would not trigger the warnings.