No damage or injuries were caused by the explosions, police said on Wednesday.
Two 60cm long steel pipes that could have been used to launch projectiles were found in the grounds of a temple near the ministry, along with batteries and a timer, but it was not clear whether any projectiles had been launched.
Police raided 30 offices and homes across the country occupied by members of a splinter group related to a left-wing association known as Kakurokyo, which claimed responsibility for a similar incident near the ministry a year ago, Kyodo news said.
Kakurokyo had in the past said it was behind attempts to fire projectiles at US military facilities in Japan.
Witnesses reported seeing flames rising from the site of the explosions, Kyodo reported.
An official at the Defence Ministry said there had been no reports of damage at the ministry, but checks were still being carried out. The explosions occurred at 23:00pm (1400 GMT).
Earlier on Tuesday, police held a large training operation simulating an armed attack on a facility in central Tokyo.
Japan approved the dispatch of its main army contingent to help rebuild Iraq in late January, and now has 100 troops establishing a base in Samawa in southern Iraq.
It plans to send up to 600 ground troops in a total deployment in Iraq of about 1000, including air force and navy personnel.
Support for Japanese PM Junichiro
Koizumi seems to be growing
Critics have argued the deployment violates Japan's pacifist constitution, but an opinion poll reported in business daily Nihon Keizai on Monday said support for Prime Minister Junichiro Koizumi had risen this year, suggesting growing public acceptance of his decision to send troops to Iraq.
Japanese leftists have in the past used steel pipes as home-made launchers to fire projectiles at police or government facilities and US military bases.
The National Police Agency said in December Japan's close ties with the United States and the many US facilities in the country could make it a target for attacks by militants.
Japan is one of the United States' closest allies in Asia and is host to about half the approximately 100,000 US military personnel in the region. Many US companies have a substantial presence in the country.