Swiss-based Armani had argued that the registered owner of the address, Anand Mani, a graphic designer based in Vancouver, had taken the name with intent to confuse - a phenomenon known as cybersquatting.
But Mr Mani argued because his business had operated under the name A.R.Mani since 1981, he had at least as much right to the address as the fashion company.
A panel of the World Intellectual Property Organization (WIPO), a United Nations body, cleared Mr Mani of cybersquatting, and dismissed Armani's complaint.
The fashion house, which is owned by holding company GA Modefine, had failed to come up with any concrete evidence that Mr Mani's use of the domain name had caused confusion, the panel said.
Fight over faith
The key element in the case, as in any dispute over domain names, is whether the name was registered in bad faith.
Popstar Madonna, actresses Julia Roberts and Nicole Kidman, and authors Julian Barnes and Louis de Bernières are among figures who have won control over web addresses bearing their names.
But rock star Bruce Springsteen lost an attempt to evict a fan club from the internet address brucespringsteen.com.
The club, the Bruce Springsteen Club, was considered to have a legitimate right to the address.
In cases where a number of claims of legitimate ownership are made, authorities have generally sided with the company or individual that moved first.
No prior claim
Armani's lawyers argued that Mr Mani could have alternative names such as anandrmani.com.
But while the panel agreed, it ruled that Armani had no prior claim over the name, even though its business was far more high-profile than Mr Mani's.
As of 2 August, however, Mr Mani's armani.com web address was not in operation.
The United Nations WIPO arbitration system was started in 1999 to help clear up a rash of arguments over internet domain names.
Before then, many people made a fortune by registering the domain names of companies or famous people, and then offering to sell them back for exorbitant sums.