diff --git a/demo/markdownlint-browser.js b/demo/markdownlint-browser.js
index 0fe2b1cb..d994a920 100644
--- a/demo/markdownlint-browser.js
+++ b/demo/markdownlint-browser.js
@@ -3211,6 +3211,7 @@ var emphasisRe = /(^|[^\\]|\\\\)(?:(\*\*?\*?)|(__?_?))/g;
 var asteriskListItemMarkerRe = /^([\s>]*)\*(\s+)/;
 var leftSpaceRe = /^\s+/;
 var rightSpaceRe = /\s+$/;
+var tablePipeRe = /\|/;
 module.exports = {
     "names": ["MD037", "no-space-in-emphasis"],
     "description": "Spaces inside emphasis markers",
@@ -3227,7 +3228,7 @@ module.exports = {
             pendingError = null;
         }
         // eslint-disable-next-line jsdoc/require-jsdoc
-        function handleRunEnd(line, lineIndex, contextLength, match, matchIndex) {
+        function handleRunEnd(line, lineIndex, contextLength, match, matchIndex, inTable) {
             // Close current run
             var content = line.substring(emphasisIndex, matchIndex);
             if (!emphasisLength) {
@@ -3238,7 +3239,8 @@ module.exports = {
             }
             var leftSpace = leftSpaceRe.test(content);
             var rightSpace = rightSpaceRe.test(content);
-            if (leftSpace || rightSpace) {
+            if ((leftSpace || rightSpace) &&
+                (!inTable || !tablePipeRe.test(content))) {
                 // Report the violation
                 var contextStart = emphasisIndex - emphasisLength;
                 var contextEnd = matchIndex + contextLength;
@@ -3308,7 +3310,7 @@ module.exports = {
                             addErrorContext.apply(void 0, pendingError);
                             pendingError = null;
                         }
-                        var error = handleRunEnd(line, lineIndex, effectiveEmphasisLength, match, matchIndex);
+                        var error = handleRunEnd(line, lineIndex, effectiveEmphasisLength, match, matchIndex, inTable);
                         if (error) {
                             // @ts-ignore
                             addErrorContext.apply(void 0, error);
@@ -3342,7 +3344,7 @@ module.exports = {
             }
             if (emphasisIndex !== -1) {
                 pendingError = pendingError ||
-                    handleRunEnd(line, lineIndex, 0, null, line.length);
+                    handleRunEnd(line, lineIndex, 0, null, line.length, inTable);
                 // Adjust for pending run on new line
                 emphasisIndex = 0;
                 emphasisLength = 0;
diff --git a/lib/md037.js b/lib/md037.js
index 850639ab..34a4d0e0 100644
--- a/lib/md037.js
+++ b/lib/md037.js
@@ -10,6 +10,7 @@ const emphasisRe = /(^|[^\\]|\\\\)(?:(\*\*?\*?)|(__?_?))/g;
 const asteriskListItemMarkerRe = /^([\s>]*)\*(\s+)/;
 const leftSpaceRe = /^\s+/;
 const rightSpaceRe = /\s+$/;
+const tablePipeRe = /\|/;
 
 module.exports = {
   "names": [ "MD037", "no-space-in-emphasis" ],
@@ -28,7 +29,9 @@ module.exports = {
       pendingError = null;
     }
     // eslint-disable-next-line jsdoc/require-jsdoc
-    function handleRunEnd(line, lineIndex, contextLength, match, matchIndex) {
+    function handleRunEnd(
+      line, lineIndex, contextLength, match, matchIndex, inTable
+    ) {
       // Close current run
       let content = line.substring(emphasisIndex, matchIndex);
       if (!emphasisLength) {
@@ -39,7 +42,10 @@ module.exports = {
       }
       const leftSpace = leftSpaceRe.test(content);
       const rightSpace = rightSpaceRe.test(content);
-      if (leftSpace || rightSpace) {
+      if (
+        (leftSpace || rightSpace) &&
+        (!inTable || !tablePipeRe.test(content))
+      ) {
         // Report the violation
         const contextStart = emphasisIndex - emphasisLength;
         const contextEnd = matchIndex + contextLength;
@@ -111,7 +117,13 @@ module.exports = {
                 pendingError = null;
               }
               const error = handleRunEnd(
-                line, lineIndex, effectiveEmphasisLength, match, matchIndex);
+                line,
+                lineIndex,
+                effectiveEmphasisLength,
+                match,
+                matchIndex,
+                inTable
+              );
               if (error) {
                 // @ts-ignore
                 addErrorContext(...error);
@@ -141,7 +153,7 @@ module.exports = {
         }
         if (emphasisIndex !== -1) {
           pendingError = pendingError ||
-            handleRunEnd(line, lineIndex, 0, null, line.length);
+            handleRunEnd(line, lineIndex, 0, null, line.length, inTable);
           // Adjust for pending run on new line
           emphasisIndex = 0;
           emphasisLength = 0;
diff --git a/test/spaces_inside_emphasis_markers.md b/test/spaces_inside_emphasis_markers.md
index 8998ec62..237c15ad 100644
--- a/test/spaces_inside_emphasis_markers.md
+++ b/test/spaces_inside_emphasis_markers.md
@@ -313,3 +313,31 @@ text [reference*link] star * star text
 *** text
 **text**
 ***
+
+| Table | Table |
+| ----- | ----- |
+| star  | x * y |
+| under | x _ y |
+
+| Table | Table |
+| ----- | ----- |
+| star  | x * y |
+| star  | x * y |
+| under | x _ y |
+| under | x _ y |
+
+| Table | Table                     |
+| ----- | ------------------------- |
+| star  | text *text* text          |
+| star  | text * text* text {MD037} |
+| star  | text *text * text {MD037} |
+| under | text _text_ text          |
+| under | text _ text_ text {MD037} |
+| under | text _text _ text {MD037} |
+
+| Table | Table |
+| ----- | ----- |
+| x * y | x * y |
+| x** y | x** y |
+| x _ y | x _ y |
+| x__ y | x__ y |