The group – calling themselves the F**k the War Coalition – destroyed at least ten windows at the Selex Galileo site at Crewe Toll, apparently using ball bearings.
Police were called to the incident and are still investigating.
Campaigners from the group contacted the Evening News at 3am to claim responsibility, protesting against the company's involvement in the UK's defence programme.
Selex Galileo is responsible for making defence systems and security applications and employs more than 7000 people across the UK, Italy and the United States and has been a target for campaign groups in the past.
The campaigners' e-mail said: "We are bringing the war home to those who profit from imperialism.
"This morning we broke windows on the Selex Galileo building.
"Corporations like Selex Galileo play a vital role in the military industrial complex. They have the blood of the innocent Afghani, Iraqi and Palestinian people who suffer at the hands of the capitalist system."
It went on: "The war in Afghanistan has nothing to do with democracy, women's rights, opium or the war on terror.
"It's about oil pipelines, making money for big corporations and establishing permanent military bases near China, India and Pakistan.
"Working class people from Scotland are joining the Army and getting killed in Afghanistan so that the bosses and shareholders of companies like Selex and BP can make more money."
The group targeted the administrative block of Selex Galileo, which has two sites on Crewe Road North, smashing windows at the back of the building.
A cordon had been places around the area this morning as hundreds of workers made their way into the building.
It is not yet known how much the damage has cost the company.
A spokesman for Lothian and Borders Police said: "There has been a report of vandalism at the premises. Officers are still dealing with it."
Organisers behind the attack told the Evening News the campaign group "does not exist" and is rather "a name used by those taking action against the war machine".
One of those involved said: "Property destruction and other acts of direct action have been claimed by the FTWC across the UK for the last two and-a-half years and will continue until global militarism has ceased."
The "FTWC have attacked army recruitment centres, arms factories, and the American consulates and embassies."
In July 2007, anti-war protesters claimed responsibility for a series of attacks at the Selex plant in Ferry Road.
A group describing itself as an anti-war coalition used a series of anonymous articles on the IndyMedia Scotland website to say it had carried out three attacks, in which windows were smashed.
The attack was linked to similar attacks in March that year on the offices of Edinburgh MPs Nigel Griffiths and Alistair Darling.
In April, an armed forces recruitment centre on Shandwick Place had windows smashed and was daubed with anti-war slogans. The following month red paint was thrown at the US consulate in Regent Terrace and a week later, yellow paint was thrown at the German consulate in Haymarket.