Amnesty International swiftly condemned the move as "alarming" and urged Qatari authorities to "immediately reverse the blocking of Doha News".
A censorship row is likely to be embarrassing for the Qatari authorities as they face constant international scrutiny after controversially winning the right to host the 2022 football World Cup.
Doha News, which published several sensitive articles earlier this year, said it had been inaccessible to most online users for almost 24 hours.
"We can only conclude that our website has been deliberately targeted and blocked by Qatar authorities," the website's management said in a statement.
"We are incredibly disappointed with this decision, which appears to be an act of censorship.
"We believe strongly in the importance of a free press, and are saddened that Qatar, home of the Doha Center for Media Freedom and Al-Jazeera, has decided to take this step."
The website, which says it has an audience of around one million unique users per month, was seemingly blocked by the country's Internet service providers, Ooredoo and Vodafone, on Wednesday.
Signup to our newsletter and follow us on Facebook and Twitter!
Neither provider responded to requests for comment from AFP.
Access was bocked on mobiles and computers, although some people could still visit the site using a virtual private network (VPN).
The website then created another domain name for its readers, but that too stopped working.
The deputy director of London-based Amnesty International, James Lynch, said the move was "an alarming setback for freedom of expression in the country".
"Deliberately blocking people in Qatar from accessing a legitimate news website would be an outright attack on media freedom," he said in a statement.
Founder of Al-Jazeera and host of a centre dedicated to promoting global media freedom, "Qatar should be at the forefront of those championing freedom of the press.
"Instead, the government appears to have specifically targeted a key source of independent and credible journalism in the country, which has played an important role in fostering dialogue and discussion about social and political issues," he said.
Two months ago, Doha News carried an editorial which charged that Qatar's cybercrime law was being used to "silence" people.
In the summer, it published an anonymous article by a gay Qatari man. Homosexuality is illegal in the emirate.