diff --git a/NEWS.md b/NEWS.md
index 7a6e93aa02..95d5131a8d 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,7 @@
 # dplyr 0.4.3.9000
 
+* `tbl_df` automatically generates column names (#1606). 
+
 * `mutate` failed to deep copy data that ends up in a list column (#1643).  
 
 * `mutate` handles adding a factor that is all `NA` (#1645).
diff --git a/src/matrixToDataFrame.cpp b/src/matrixToDataFrame.cpp
index 6008f788f8..4da4748b80 100644
--- a/src/matrixToDataFrame.cpp
+++ b/src/matrixToDataFrame.cpp
@@ -1,10 +1,7 @@
 #include <Rcpp.h>
 using namespace Rcpp;
 
-// [[Rcpp::export]]
-List matrixToDataFrame(RObject x) {
-  SEXPTYPE type = TYPEOF(x);
-
+IntegerVector get_dim( const RObject& x){
   if (!x.hasAttribute("dim"))
     stop("`x` is not a matrix");
 
@@ -12,6 +9,33 @@ List matrixToDataFrame(RObject x) {
   if (dim.size() != 2)
     stop("`x` is not a matrix");
 
+  return dim ;
+}
+
+CharacterVector get_names( const RObject& x, const IntegerVector& dim){
+  int nc = dim[1] ;
+  if( x.hasAttribute("dimnames") ){
+    List dimnames = x.attr("dimnames") ;
+    try {
+      CharacterVector res( dimnames[1] ) ;
+      return res ;
+    } catch(...){}
+  }
+
+  CharacterVector names( nc ) ;
+  for( int i=0; i<nc; i++){
+    names[i] = tfm::format( "V%d", (i+1) ) ;
+  }
+  return names ;
+}
+
+// [[Rcpp::export]]
+List matrixToDataFrame(RObject x) {
+  SEXPTYPE type = TYPEOF(x);
+
+  IntegerVector dim = get_dim(x) ;
+  CharacterVector names = get_names(x, dim) ;
+
   int nrow = dim[0], ncol = dim[1];
 
   List out = List(ncol);
@@ -42,11 +66,7 @@ List matrixToDataFrame(RObject x) {
     }
   }
 
-  if (x.hasAttribute("dimnames")) {
-    List dimnames = x.attr("dimnames");
-    out.attr("names") = dimnames[1];
-  }
-
+  out.attr("names") = names ;
   out.attr("class") = CharacterVector::create("tbl_df", "tbl", "data.frame");
   out.attr("row.names") = IntegerVector::create(NA_INTEGER, -nrow);
 
diff --git a/tests/testthat/test-data_frame.R b/tests/testthat/test-data_frame.R
index 82c1776f11..6f5d6dbf1a 100644
--- a/tests/testthat/test-data_frame.R
+++ b/tests/testthat/test-data_frame.R
@@ -82,3 +82,17 @@ test_that("names must be unique (#820)", {
     "Each variable must have a unique name"
   )
 })
+
+test_that("data frame column names are automatically generated (#1606)", {
+  m <- matrix( 1:6, nr = 3)
+  df <- tbl_df(m)
+  expect_equals( names(df), c("V1", "V2") )
+
+  row.names(m) <- 1:3
+  df <- tbl_df(m)
+  expect_equals( names(df), c("V1", "V2") )
+
+  colnames(m) <- c("a", "b")
+  df <- tbl_df(m)
+  expect_equals( names(df), c("a", "b") )
+})