When you upload pictures to your Facebook profile, the pictures display on your profile and your friends' news feed pages automatically, allowing your friends to view and comment on them. When you want to prevent others from posting comments on your pictures, you must delete the comments as they appear or edit your privacy settings. Your privacy settings allow you to make the pictures private or block specific friends from viewing and commenting on the picture.
Log in to your Facebook account and click "Account" from the upper right corner of your News Feed page.
Click "Privacy Settings" from the drop-down list.
Click "Customize Settings" under the Sharing on Facebook section.
Click the button next to "Permission to Comment on Your Posts" in the Things Others Share section, and click "Customize." A dialog box appears on your screen.
Change the setting in the Make This Visible To section to "Only Me." Changing this setting prevents all friends from viewing and posting comments to your pictures. Alternatively, type the name of a friend in the "Hide this From" field and press "Enter." Adding people to the list prevents specific friends from viewing and posting comments to your pictures.
Click "Save Settings" and close the dialog box.
Log in to your Facebook account and click "Profile" from the upper right corner of your News Feed page.
Click "Photos" from the left column of your profile.
Click the album that contains the picture with the comment that you want to delete and click the picture.
Hover your mouse over the comment that you want to delete and click the "X" that appears in the upper right corner.
Click "Remove Comment" and click "Delete." The comment disappears from your picture, preventing anyone from viewing it.