Cat Rock Capital said the "last-minute" probe by the Competitions and Markets Authority (CMA) was “shocking and clearly unwarranted”.
The US-based firm owns 3% of Just Eat’s shares and 6% of Takeaway.com’s shares.
Earlier this month Dutch giant Takeaway.com beat rival bidder Prosus to secure the c.£6bn merger with Just Eat after months of counterbids.
The deal, approved by 90% shareholders, creates one of the world’s largest meal delivery companies.
The CMA announced yesterday (24 January) it was beginning an investigation in to the merger, the first phase of which will conclude on 6 February.
Cat Rock has accused the CMA of drawing a “false equivalence” between the tie-up and Amazon’s investment in Deliveroo, which the watchdog is probing over fears it would reduce competition by discouraging Amazon from relaunching its own restaurant delivery service.
Alex Captain, founder of Cat Rock, said it was “patently absurd” to compare the two.
“Amazon has a large UK business with millions of customers that it could leverage to re-enter the UK online food delivery market and increase competition,” he said.
“Takeaway.com has no UK operations, exited its minor business there over three years ago, and has stated it had no intention to enter the UK market before the Just Eat merger.”
He added that the combined company would have a greater chance of competing against “dominant global technology” firms such as Amazon and Uber in the delivery space.
Shares in the newly merged company were due to begin trading today (24 January), but this has now been delayed a week.
Just Eat and Takeaway.com had a combined 40 million customers and processed 360 million orders in 2018.