The Dubai-based firm, which has worked with the paper for less than a year, previously handled all media sales and marketing activities for the publication after it relaunched as a tabloid at the end of last year.
Media sales will now be taken care of by an in-house team of four working directly for Emirates Evening Post.
Aldrin Fernandes, Concept Group chief executive officer, told Campaign: "There's no bad blood between us - but it's over. We put a lot of time and effort into it and we delayed some of our own titles because of spending a lot of time on the newspaper."
He added: "We expected more in terms of co-operation in the distribution of the paper and other issues, but we did not get that and so we have decided to call it a day."
Emirates Evening Post's COO, Aloke Thakore, said the relationship had ended in the best interests of the paper.
"There are things that work and things that don't work - and this didn't work out so we have decided to end it.
"We had different ideas about the distribution, but that's not to say that they were on the left and we were on the right," added Thakore.
Concept Media recently announced that it is to launch bi-monthly Gulf and Indian editions of Millionaire magazine. The 200-page magazine will cover topics ranging from shopping, events and fashion to business and health.
Readership is based on controlled distribution to 'exclusive' millionaire mailing lists and on a subscription basis only.
"With 300,000 millionaires in the Middle East with a combined wealth of US $1.2 trillion, it is easy to see why a magazine targeted at this high net worth audience should service this market," said Fernandes.