The website of the Qatari-owned global news broadcaster could not be accessed in either country on Wednesday.
Al-Thani also seems to have praised Iran which even the previous USA administration under President Obama labeled as the "biggest state sponsor of terror" as an "Islamic power" and a source of stability in the region.
KSA and UAE media outlets also considered that Doha devoted all its capabilities to be the voice of the militant groups, describing the Qatari step as a disaster.
Mr al-Thani was quoted as saying "there is no wisdom in harbouring hostility towards Iran" and that relations with the Trump administration are "tense" despite a positive meeting between the two leaders in Riyadh, the Saudi Arabia capital, last week.
An attack on the Qatar National Bank in 2016 leaked more than 1,200 customers" details into the public domain, and several "domain name poisoning' hacks on official websites in recent years have redirected traffic or illegally collected user data.
The emir also said relations with Israel are "good", and that Hamas is the official representative of Palestinians.
Sheikh Saif Bin Ahmed Al Thani, the director of the Qatar's government communications office, issued a statement saying authorities had launched an investigation. The minister was cited as ordering the removal of ambassadors from Saudi Arabia, Egypt, Kuwait, Bahrain and the UAE in response to their plotting against Qatar.
The security source said legal action would be taken against the websites, MENA reported.
"A false statement attributed to His Highness has been published", with the department saying it is investigating the issue and will hold those found responsible to account.
Saudi-owned Al Arabiya television ran a story titled "Proof that Qatar News Agency was not hacked", which noted that the statement had also run on Qatari state television and the QNA Instagram account.
"In the run-up to President Donald Trump's visit to the Middle East, an orchestrated barrage of opinion pieces by anti-Qatar organisations in a variety of mainstream and on-line publications has alleged that Qatar is sympathetic to, or turns a blind eye toward, the actions of terrorist groups in the Middle East". In 2012, a damaging virus crippled computer systems at Qatari natural gas producer RasGas soon after a similar attack on Saudi Arabia's state-run oil company.
Saudi Arabia, the UAE and Bahrain withdrew their ambassadors from Doha in 2014 after disagreements over Qatar's support for the Muslim Brotherhood boiled over.