It was down for an hour-and-a-half on Sunday morning from 10am.
A denial of service attack means the site was bombarded by traffic, which caused it to stop working, the source said.
It is not the same as hacking, in which whoever is responsible actually gets into a website and the site is compromised.
Neither the content nor the systems of the royal website were accessed on Sunday.
It is currently unknown who is responsible for the cyber attack, the source said.
The site is now up and running as usual.