The Sun claims that ex-bodyguard Quinn left the 34-year-old on April 6, her birthday.
A source reportedly close to the TV presenter said that Klass had "no idea" Quinn planned to leave her, adding that she is "heartbroken" by the news.
The pair had been in a relationship for 11 years, since Quinn became bodyguard for her ex-band Hear'Say. They married in October 2011 after a five-year engagement and have two children.
The former I'm A Celebrity contestant recently said that she and Quinn were a "tight unit", and that she takes marriage "really seriously".
Klass has been co-presenting the Jubilee Festival in Hyde Park this weekend.