Rumours of a possible break-up began swirling amid claims that Kutcher and Moore spent their sixth wedding anniversary apart last week.
Moore also posted a series of cryptic messages on Twitter, including a quote from Greek philosopher Epictetus which read: "When we are offended at any man's fault, turn to yourself and study your own failings. Then you will forget your anger."
She also tweeted an image of herself with the text description: "I see through you."
Kutcher took to Twitter this morning to post a link to his Spotify account, which was playing Public Enemy's 1988 hit 'Don't Believe the Hype'. The Spotify link wasn't accompanied by any comment from Kutcher.
Representatives for both stars haven't commented on the state of their marriage.
The couple married on September 24, 2005 in front of family and friends, including Moore's ex-husband Bruce Willis.
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Watch Public Enemy perform 'Don't Believe the Hype' below: