Index: src/wp-includes/class-wp-image-editor-imagick.php
===================================================================
--- src/wp-includes/class-wp-image-editor-imagick.php	(revision 37264)
+++ src/wp-includes/class-wp-image-editor-imagick.php	(working copy)
@@ -51,9 +51,16 @@
 		if ( ! extension_loaded( 'imagick' ) || ! class_exists( 'Imagick', false ) || ! class_exists( 'ImagickPixel', false ) )
 			return false;
 
-		if ( version_compare( phpversion( 'imagick' ), '2.2.0', '<' ) )
+		$imagick_version = phpversion( 'imagick' );
+		if ( version_compare( $imagick_version, '2.2.0', '<' ) ) {
 			return false;
+		}
 
+		// Imagick 3.4 is throwing exceptions in PHP 7, see https://core.trac.wordpress.org/ticket/36587.
+		if ( version_compare( $imagick_version, '3.4', '>=' ) && version_compare( $imagick_version, '3.4.2', '<' ) ) {
+			return false;
+		}
+
 		$required_methods = array(
 			'clear',
 			'destroy',