diff --git a/tokio/src/future/maybe_done.rs b/tokio/src/future/maybe_done.rs
index 506b4f26c18..8b270b3a01f 100644
--- a/tokio/src/future/maybe_done.rs
+++ b/tokio/src/future/maybe_done.rs
@@ -1,7 +1,7 @@
 //! Definition of the [`MaybeDone`] combinator.
 
 use pin_project_lite::pin_project;
-use std::future::Future;
+use std::future::{Future, IntoFuture};
 use std::pin::Pin;
 use std::task::{Context, Poll};
 
@@ -22,8 +22,10 @@ pin_project! {
 }
 
 /// Wraps a future into a `MaybeDone`.
-pub fn maybe_done<Fut: Future>(future: Fut) -> MaybeDone<Fut> {
-    MaybeDone::Future { future }
+pub fn maybe_done<F: IntoFuture>(future: F) -> MaybeDone<F::IntoFuture> {
+    MaybeDone::Future {
+        future: future.into_future(),
+    }
 }
 
 impl<Fut: Future> MaybeDone<Fut> {
diff --git a/tokio/src/macros/select.rs b/tokio/src/macros/select.rs
index 124d7827086..505c70dd060 100644
--- a/tokio/src/macros/select.rs
+++ b/tokio/src/macros/select.rs
@@ -495,7 +495,7 @@ doc! {macro_rules! select {
             // We can't use the `pin!` macro for this because `futures` is a
             // tuple and the standard library provides no way to pin-project to
             // the fields of a tuple.
-            let mut futures = ( $( $fut , )+ );
+            let mut futures = ( $( $crate::macros::support::IntoFuture::into_future($fut) , )+ );
 
             // This assignment makes sure that the `poll_fn` closure only has a
             // reference to the futures, instead of taking ownership of them.
diff --git a/tokio/src/macros/support.rs b/tokio/src/macros/support.rs
index 10526bcbca7..d077a0823c7 100644
--- a/tokio/src/macros/support.rs
+++ b/tokio/src/macros/support.rs
@@ -8,6 +8,6 @@ cfg_macros! {
     }
 }
 
-pub use std::future::Future;
+pub use std::future::{Future, IntoFuture};
 pub use std::pin::Pin;
 pub use std::task::Poll;
diff --git a/tokio/tests/macros_join.rs b/tokio/tests/macros_join.rs
index 37dd05f0e13..4deaf120a95 100644
--- a/tokio/tests/macros_join.rs
+++ b/tokio/tests/macros_join.rs
@@ -159,3 +159,18 @@ async fn a_different_future_is_polled_first_every_time_poll_fn_is_polled() {
 async fn empty_join() {
     assert_eq!(tokio::join!(), ());
 }
+
+#[tokio::test]
+async fn join_into_future() {
+    struct NotAFuture;
+    impl std::future::IntoFuture for NotAFuture {
+        type Output = ();
+        type IntoFuture = std::future::Ready<()>;
+
+        fn into_future(self) -> Self::IntoFuture {
+            std::future::ready(())
+        }
+    }
+
+    tokio::join!(NotAFuture);
+}
diff --git a/tokio/tests/macros_select.rs b/tokio/tests/macros_select.rs
index cbad971ab1f..c91d696426c 100644
--- a/tokio/tests/macros_select.rs
+++ b/tokio/tests/macros_select.rs
@@ -692,3 +692,20 @@ mod unstable {
         )
     }
 }
+
+#[tokio::test]
+async fn select_into_future() {
+    struct NotAFuture;
+    impl std::future::IntoFuture for NotAFuture {
+        type Output = ();
+        type IntoFuture = std::future::Ready<()>;
+
+        fn into_future(self) -> Self::IntoFuture {
+            std::future::ready(())
+        }
+    }
+
+    tokio::select! {
+        () = NotAFuture => {},
+    }
+}