diff --git a/R/data-mask.R b/R/data-mask.R
index b72a708289..5b04db7091 100644
--- a/R/data-mask.R
+++ b/R/data-mask.R
@@ -11,7 +11,16 @@ DataMask <- R6Class("DataMask",
       frame <- caller_env(n = 2)
       local_mask(self, frame)
 
-      names_bindings <- chr_unserialise_unicode(names2(data))
+      names <- names(data)
+
+      if (is.null(names)) {
+        abort("Can't transform a data frame with `NULL` names.")
+      }
+      if (vec_any_missing(names)) {
+        abort("Can't transform a data frame with missing names.")
+      }
+
+      names_bindings <- chr_unserialise_unicode(names)
       if (any(names_bindings == "")) {
         # `names2()` converted potential `NA` names to `""` already
         abort("Can't transform a data frame with `NA` or `\"\"` names.", call = error_call)
diff --git a/tests/testthat/test-data-mask.R b/tests/testthat/test-data-mask.R
new file mode 100644
index 0000000000..675f8001a9
--- /dev/null
+++ b/tests/testthat/test-data-mask.R
@@ -0,0 +1,7 @@
+test_that("Empty matrix can be coerced to a data frame (#7004)", {
+  skip_if_not(getRversion() >= "4.4")
+  expect_error(
+    slice(as.data.frame(matrix(nrow = 0, ncol = 0)), 1),
+    NA
+  )
+})