diff --git a/include/data.h b/include/data.h
index 32fb098f..f55e003d 100644
--- a/include/data.h
+++ b/include/data.h
@@ -477,6 +477,10 @@ struct Window {
     int min_width;
     int min_height;
 
+    /* Maximum size specified for the window. */
+    int max_width;
+    int max_height;
+
     /* aspect ratio from WM_NORMAL_HINTS (MPlayer uses this for example) */
     double aspect_ratio;
 };
diff --git a/src/floating.c b/src/floating.c
index fac14a7a..be514ce2 100644
--- a/src/floating.c
+++ b/src/floating.c
@@ -96,6 +96,18 @@ void floating_check_size(Con *floating_con) {
             floating_con->rect.height += border_rect.height;
         }
 
+        if (focused_con->window->max_width) {
+            floating_con->rect.width -= border_rect.width;
+            floating_con->rect.width = min(floating_con->rect.width, focused_con->window->max_width);
+            floating_con->rect.width += border_rect.width;
+        }
+
+        if (focused_con->window->max_height) {
+            floating_con->rect.height -= border_rect.height;
+            floating_con->rect.height = min(floating_con->rect.height, focused_con->window->max_height);
+            floating_con->rect.height += border_rect.height;
+        }
+
         if (focused_con->window->height_increment &&
             floating_con->rect.height >= focused_con->window->base_height + border_rect.height) {
             floating_con->rect.height -= focused_con->window->base_height + border_rect.height;
diff --git a/src/handlers.c b/src/handlers.c
index d1b3a73c..d2232965 100644
--- a/src/handlers.c
+++ b/src/handlers.c
@@ -981,9 +981,18 @@ static bool handle_normal_hints(void *data, xcb_connection_t *conn, uint8_t stat
         con->window->min_height = size_hints.min_height;
     }
 
+    if ((size_hints.flags & XCB_ICCCM_SIZE_HINT_P_MAX_SIZE)) {
+        DLOG("Maximum size: %d (width) x %d (height)\n", size_hints.max_width, size_hints.max_height);
+
+        con->window->max_width = size_hints.max_width;
+        con->window->max_height = size_hints.max_height;
+    }
+
     if (con_is_floating(con)) {
         win_width = MAX(win_width, con->window->min_width);
         win_height = MAX(win_height, con->window->min_height);
+        win_width = MIN(win_width, con->window->max_width);
+        win_height = MIN(win_height, con->window->max_height);
     }
 
     bool changed = false;
diff --git a/src/manage.c b/src/manage.c
index f97ecc62..4031ade6 100644
--- a/src/manage.c
+++ b/src/manage.c
@@ -520,6 +520,12 @@ void manage_window(xcb_window_t window, xcb_get_window_attributes_cookie_t cooki
         nc->window->min_height = wm_size_hints.min_height;
     }
 
+    if (wm_size_hints.flags & XCB_ICCCM_SIZE_HINT_P_MAX_SIZE) {
+        DLOG("Window specifies maximum size %d x %d\n", wm_size_hints.max_width, wm_size_hints.max_height);
+        nc->window->max_width = wm_size_hints.max_width;
+        nc->window->max_height = wm_size_hints.max_height;
+    }
+
     /* Store the requested geometry. The width/height gets raised to at least
      * 75x50 when entering floating mode, which is the minimum size for a
      * window to be useful (smaller windows are usually overlays/toolbars/…
diff --git a/testcases/t/189-floating-constraints.t b/testcases/t/189-floating-constraints.t
index 6b082bfd..4ac95e15 100644
--- a/testcases/t/189-floating-constraints.t
+++ b/testcases/t/189-floating-constraints.t
@@ -21,6 +21,7 @@
 #
 
 use i3test i3_autostart => 0;
+use X11::XCB qw/PROP_MODE_REPLACE/;
 
 ################################################################################
 # 1: check floating_minimum_size (with non-default limits)
@@ -218,4 +219,82 @@ is($rect->{height}, 70, 'height did not exceed minimum height');
 
 exit_gracefully($pid);
 
+################################################################################
+# 8: check minimum_size and maximum_size set by WM_NORMAL_HINTS
+################################################################################
+
+$config = <<EOT;
+# i3 config file (v4)
+font -misc-fixed-medium-r-normal--13-120-75-75-C-70-iso10646-1
+EOT
+
+my $min_width = 150;
+my $min_height = 100;
+my $max_width = 250;
+my $max_height = 200;
+
+my sub open_with_max_size {
+    # The type of the WM_NORMAL_HINTS property is WM_SIZE_HINTS
+    # https://tronche.com/gui/x/icccm/sec-4.html#s-4.1.2.3
+    my $XCB_ICCCM_SIZE_HINT_P_MIN_SIZE = 0x32;
+    my $XCB_ICCCM_SIZE_HINT_P_MAX_SIZE = 0x16;
+
+    my $flags = $XCB_ICCCM_SIZE_HINT_P_MIN_SIZE | $XCB_ICCCM_SIZE_HINT_P_MAX_SIZE;
+
+    my $pad = 0x00;
+
+    my $window = open_window(
+        before_map => sub {
+            my ($window) = @_;
+
+            my $atomname = $x->atom(name => 'WM_NORMAL_HINTS');
+            my $atomtype = $x->atom(name => 'WM_SIZE_HINTS');
+            $x->change_property(
+                PROP_MODE_REPLACE,
+                $window->id,
+                $atomname->id,
+                $atomtype->id,
+                32,
+                13,
+                pack('C5N8', $flags, $pad, $pad, $pad, $pad, 0, 0, 0, $min_width, $min_height, $max_width, $max_height),
+            );
+        },
+    );
+
+    return $window;
+}
+
+my sub check_minsize {
+    is($window->rect->{width}, $min_width, 'width = min_width');
+    is($window->rect->{height}, $min_height, 'height = min_height');
+}
+
+my sub check_maxsize {
+    is($window->rect->{width}, $max_width, 'width = max_width');
+    is($window->rect->{height}, $max_height, 'height = max_height');
+}
+
+$pid = launch_with_config($config);
+
+$window = open_with_max_size;
+cmd 'floating enable';
+cmd 'border none';
+sync_with_i3;
+
+cmd "resize set $min_width px $min_height px";
+check_minsize;
+
+# Try to resize below minimum width
+cmd 'resize set ' . ($min_width - 10) . ' px ' . ($min_height - 50) . ' px';
+check_minsize;
+
+cmd "resize set $max_width px $max_height px";
+check_maxsize;
+
+# Try to resize above maximum width
+cmd 'resize set ' . ($max_width + 150) . ' px ' . ($max_height + 500) . ' px';
+check_maxsize;
+
+exit_gracefully($pid);
+
 done_testing;