The aviation regulator said it hads taken "urgent action" over the suspicious online activity and would inform the police.
It has added further verification checks to its refund process and pledged to seek prosecutions where there is evidence of deception.
Around 100,000 claims have been made since the website went live on Monday morning.
It was set up to enable people with Atol-protected bookings for Thomas Cook holidays due to begin after the firm collapsed on 23 September to obtain refunds.
This relates to more than 360,000 bookings covering trips set to be taken by 800,000 people.
The CAA is aiming to pay refunds within 60 days of receiving a valid form and wants to crack down on fraudulent activity to avoid any delay.
Dame Deirdre Hutton, who chairs the organisation, said: "This morning we have taken urgent action in response to what we believe is attempted fraudulent activity in relation to refunds for Thomas Cook customers.
"If you have made a claim directly with us, then your claim is being processed and you do not need to take any action."
She added: "Please help us to combat the risk of fraud by not submitting your details to any other website.
"Our focus is on getting money back to the right people as soon as possible and combating fraud in every way possible."
The CAA was forced to apologise on Monday after its system struggled to cope with "unprecedented demand" in the hours after it launched.
Many people received an error message after entering their details, meaning their claims were not submitted.
Consumers affected by the collapse of Thomas Cook can find out more information at https://thomascook.caa.co.uk/.