The official site, regeringen.se, was offline for several hours overnight and only a message saying the site could not be reached was visible.
Commercial websites including Visa, MasterCard and PayPal have already been targeted by co-ordinated action on one of the busiest shopping days of the year after the firms said that they would no longer process donations to WikiLeaks.
A group calling itself Anonymous and operating under the banner "Operation Payback" was behind some of the attacks and there were concerns that Twitter could become a target because it removed Anonymous’ listing.
A 22-year-old software engineer who called himself Coldblood said: "The campaign is not over, it’s still going strong. More and more people are joining.
"I see this as becoming a war – but not a traditional war: this is a war of data."
He added: "We are trying to keep the internet free for everyone."
The actions so far have been essentially attacks by volume, known as DDoS or distributed denial of service, in which the target site is hit with massively increased numbers of visitors with the intention of exceeding its capabilities and forcing it to crash.
In this case, hundreds of volunteers have downloaded something called a botnet, which aids the distribution of the command to attack the site. The volunteers wait until they are given a signal on an internet chatroom, before launching the massed attack.
The attacks are illegal in Britain and carry a maximum sentence of two years.
Carole Theriault, a senior security consultant at Sophos, a computer security firm, said: "If the big companies weren’t locking down their information before, they’re definitely doing it now.
"This is really unprecedented and Amazon could be next."
She added: "Hacking is illegal and it’s not just the companies which are the victims of this, it’s also the people who are trying to use their services to shop and the sellers of those items who can’t sell them.
However she said it was unlikely, although not impossible, for people’s credit card details to be unearthed by such attacks.
"Data held by financial services companies is extremely safe and it’s in their interests to keep it that way."
The group of "hacktivists" calling themselves Anonymous posted a blog setting out its aims as campaiging for free speech.
The post read: "Hello World. We are Anonymous. What you do or do not know about us is irrelevant. We have decided to write to you, the media, and all citizens of the free world at large to inform you of the message, our intentions, potential targets, and our ongoing peaceful campaign for freedom.
"The message is simple: freedom of speech. Anonymous is peacefully campaigning for freedom of speech everywhere in all forms. Freedom of speech for: the internet, for journalism and journalists, and citizens of the world at large. Regardless of what you think or have to say; Anonymous is campaigning for you."
One payment firm said the cyber attacks had resulted in a "complete loss of service" for its clients, although MasterCard insisted its card transactions were still secure.
A group using the Twitter handle @AnonOperation – which was linked to the WikLeaks site itself – tweeted: "Operation #Payback SITREP: www.visa.com is currently DOWN. FIRE FIRE FIRE!!!!"
The post was retweeted many times, adding to the sense that the attacks were co-ordinated, and WikiLeaks Europe declared it was at "cyberwar" on Twitter.
One tweet mocked MasterCard’s advertising slogan with the comment: "There are some things WikiLeaks can’t do. For everything else, there’s Operation Payback."
The attack in Sweden – where prosecutors issued the international warrant over alleged sex offences against Julian Assange, the WikiLeaks founder – was reported in the daily newspaper Aftonbladet.
A spokesman for MasterCard said the firm had seen "a service disruption" but insisted it had not been affected by "a concentrated effort to flood our corporate website with traffic".
A spokesman for PayPal said: "The attack slowed some payments down for a short while but we remained fully operational throughout."
Visa was thought to be unaffected by the cyberattacks.