diff --git a/docs/release-notes/3980.fix.md b/docs/release-notes/3980.fix.md
new file mode 100644
index 0000000000..b5ec7c6fcb
--- /dev/null
+++ b/docs/release-notes/3980.fix.md
@@ -0,0 +1 @@
+Prevent segfault when running {func}`scanpy.pp.highly_variable_genes` with `flavor='seurat_v3{,_paper}'` and some all-zero genes {smaller}`P Angerer`
diff --git a/src/scanpy/_compat.py b/src/scanpy/_compat.py
index c2e26412e8..11b0704328 100644
--- a/src/scanpy/_compat.py
+++ b/src/scanpy/_compat.py
@@ -113,6 +113,8 @@ def warn(
     more_file_prefixes: tuple[str, ...] = (),
 ) -> None:
     """Issue a warning, skipping frames from certain file prefixes."""
+    __tracebackhide__ = True
+
     if not skip_file_prefixes:
         skip_file_prefixes = (*_FILE_PREFIXES, *more_file_prefixes)
     elif more_file_prefixes:
diff --git a/src/scanpy/preprocessing/_highly_variable_genes.py b/src/scanpy/preprocessing/_highly_variable_genes.py
index f980ac2533..906f0fb16e 100644
--- a/src/scanpy/preprocessing/_highly_variable_genes.py
+++ b/src/scanpy/preprocessing/_highly_variable_genes.py
@@ -183,14 +183,13 @@ def _highly_variable_genes_seurat_v3(  # noqa: PLR0912, PLR0915
         # These get computed anyway for loess
         if isinstance(mean, DaskArray):
             mean, var = mean.compute(), var.compute()
-        not_const = var > 0
         estimat_var = np.zeros(data.shape[1], dtype=np.float64)
-
-        y = np.log10(var[not_const])
-        x = np.log10(mean[not_const])
-        model = loess(x, y, span=span, degree=2)
-        model.fit()
-        estimat_var[not_const] = model.outputs.fitted_values
+        if (not_const := var > 0).any():
+            y = np.log10(var[not_const])
+            x = np.log10(mean[not_const])
+            model = loess(x, y, span=span, degree=2)
+            model.fit()
+            estimat_var[not_const] = model.outputs.fitted_values
         reg_std = np.sqrt(10**estimat_var)
 
         # clip large values as in Seurat
diff --git a/tests/test_highly_variable_genes.py b/tests/test_highly_variable_genes.py
index 847f1ae75c..670c647ab9 100644
--- a/tests/test_highly_variable_genes.py
+++ b/tests/test_highly_variable_genes.py
@@ -10,6 +10,7 @@
 import numpy as np
 import pandas as pd
 import pytest
+import scipy.sparse as sps
 from anndata import AnnData
 from fast_array_utils import stats
 from pandas.testing import assert_frame_equal, assert_index_equal
@@ -522,6 +523,15 @@ def test_seurat_v3_warning():
         sc.pp.highly_variable_genes(pbmc, flavor="seurat_v3")
 
 
+@needs.skmisc
+def test_seurat_v3_degenerate() -> None:
+    """Tests that the flavor handles all-zero genes."""
+    adata = AnnData(sps.random(10, 1000, density=0.001, format="csr", dtype="int"))
+    adata.X.data = np.abs(adata.X.data)
+
+    sc.pp.highly_variable_genes(adata, flavor="seurat_v3")
+
+
 def test_batches():
     adata = pbmc68k_reduced()
     adata.X[:100, :100] = np.zeros((100, 100))