The 38-year-old shared the news on Instagram on Sunday.
"It has brought us such happiness to walk together, but the time has come for Joe and I to part ways and walk on, apart" she wrote.
"We ask for your kindness and consideration for our privacy, we will not be making any further comment as our private lives have, and will always remain exactly that.
"We wish you peace at the end of such a challenging year for all."
Melissa shared earlier this year she and Joe were married after only five months of dating, because "when you know, you know".
"I first met him briefly at his bar in Melbourne, Romeo Lane," she told TV Week.
"Then we met again properly about 18 months later at a function. We started talking there and we've just not ever ceased since really. It's pretty cool."
Melissa was filming her show The Chef's Line when the pair mutually decided to get married three months into their relationship.
"I planned our elopement in between takes while filming another TV show," she told the publication.
"When that wrapped, we went to Joshua Tree in California and eloped. It was all very fun."
Earlier this year, when the pair celebrated their third anniversary, Melissa shared a tribute to her husband, writing, "It was probably a sign that [Joe] and my wedding photos look cinematic, because life since then has been a non-stop blockbuster of action, drama, comedy... and of course romance. 3 years married to you feels like a lifetime, and a split second at the same time."
The pair share a cat called Ghost together.
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