diff --git a/NEWS.md b/NEWS.md
index 1715a4c82f..6c444cd08f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -8,6 +8,7 @@
 * Fixed spurious warnings from `sec_axis()` with `breaks = NULL` (#5713).
 * Patterns and gradients are now also enabled in `geom_sf()` 
   (@teunbrand, #5716).
+* `stat_bin()` deals with non-finite breaks better (@teunbrand, #5665).
 
 # ggplot2 3.5.0
 
diff --git a/R/bin.R b/R/bin.R
index 5cb1a948ee..8ca4bff921 100644
--- a/R/bin.R
+++ b/R/bin.R
@@ -1,10 +1,14 @@
 bins <- function(breaks, closed = "right",
-                 fuzz = 1e-08 * stats::median(diff(breaks))) {
+                 fuzz = NULL) {
   check_numeric(breaks)
   closed <- arg_match0(closed, c("right", "left"))
-
   breaks <- sort(breaks)
+
   # Adapted base::hist - this protects from floating point rounding errors
+  fuzz <- fuzz %||% 1e-08 * stats::median(diff(breaks[is.finite(breaks)]))
+  if (!is.finite(fuzz)) { # happens when 0 or 1 finite breaks are given
+    fuzz <- .Machine$double.eps * 1e3
+  }
   if (closed == "right") {
     fuzzes <- c(-fuzz, rep.int(fuzz, length(breaks) - 1))
   } else {
diff --git a/tests/testthat/test-stat-bin.R b/tests/testthat/test-stat-bin.R
index d15a19fcff..6ab5ec96b2 100644
--- a/tests/testthat/test-stat-bin.R
+++ b/tests/testthat/test-stat-bin.R
@@ -112,6 +112,13 @@ test_that("stat_bin() provides width (#3522)", {
 
 # Underlying binning algorithm --------------------------------------------
 
+test_that("bins() computes fuzz with non-finite breaks", {
+  test <- bins(breaks = c(-Inf, 1, Inf))
+  expect_equal(test$fuzzy, test$breaks, tolerance = 1e-10)
+  difference <- test$fuzzy - test$breaks
+  expect_equal(difference[2], 1000 * .Machine$double.eps, tolerance = 0)
+})
+
 comp_bin <- function(df, ...) {
   plot <- ggplot(df, aes(x = x)) + stat_bin(...)
   layer_data(plot)