Just before 2.30pm on Friday, websites for the Riksbank, the Swedish Institute, and security service Säpo were all inaccessible.
The website for the Riksdag was also inaccessible for a short time.
Other sites hit in the apparent attack included that of the Svea Court of Appeal, as well as the police, and the Swedish courts.
While some of the sites remained down for extended periods of time, others were slow to load or were intermittently offline.
The website for the Prison and Probation Service (Kriminalvården) was not fully functioning, but a spokesperson told The Local that the site was undergoing maintenance which began before the attack occurred.
The outages coincide with the time mentioned in a video warning about cyber attacks to be launched against Sweden and which was issued earlier this week by someone claiming to speak for Anonymous.
“This Friday we will do the biggest thing we have ever done. We will not say what we will do yet,” an artificial sounding voice proclaimed in the clip, which claims ties to Anonymous and was broadcast on YouTube.
Per Gårdehall, webmaster at for the Swedish Institute, confirmed that the organization's website, www.sweden.se, had also been targeted in the attack.
“Yes, we have been down for almost two hours now, they started early with us at around 12.30pm. We expect it's another DDOS attack,” he told The Local.
“I guess it's the Anonymous network again. We'll most likely formally report this to the police next week.”
During a DDOS attack, a website is bombarded with communication requests so that the servers become overloaded and the site crashes, and late Wednesday night the Riksbank's website was inaccessible.
Details of the attack were being discussed freely on Facebook by people claiming to be a part of Anonymous.
A total of 18 websites were listed as potential targets for the attack, which was scheduled to begin at 2.30pm local time and continue for much of the afternoon.
A Facebook group featuring details of the attack has almost 2,000 members and encourages people to help in carrying out the cyber attack.
“Let's start attack on Swedish Sites!” the page reads, followed by a list of “targets” containing 18 official Swedish government agency websites, and a warning that the attack will begin at 2.30pm.
The Facebook group, called #OpPRK #OpPirateBay, also features links to the two videos uploaded to YouTube by the Anonymous group.
In the second video, posted online on Thursday, an Anonymous spokesperson in a mask speaks to the camera in an automated voice.
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“In the next coming days, Anonymous will become even more active and launch major attacks on several vital portals that represent Swedish society,” the voice reads.
The video claims the attack will be the "biggest thing ever done" by Anonymous and closes with a warning that "the internet belongs to us".
According to the clips posted on YouTube earlier in the week, the attacks are meant to be a retaliation against Monday's raid by Swedish police on web hosts PRQ, previously hosting both The Pirate Bay and WikiLeaks.
Police confiscated three servers in the raid, including those hosting filesharing site Tankafetest.se