In May, Amazon led a $575m (£450m) investment round in the food delivery app raising a $1.53bn (£1.2bn) total.
The CMA has issued an initial enforcement order while it decides whether to launch a full investigation.
At the time of the investment drive, Will Shu, founder and CEO of Deliveroo, said: “This new investment will help Deliveroo to grow and to offer customers even more choice, tailored to their personal tastes, offer restaurants greater opportunities to grow and expand their businesses, and to create more flexible, well-paid work for riders.
“Amazon has been an inspiration to me personally and to the company, and we look forward to working with such a customer-obsessed organisation. This is great news for the tech and restaurant sectors, and it will help to create jobs in all of the countries in which we operate.”