The attack took place on Monday night and the agency affiliated with the ministry was forced to close down its website, the ministry said.
The hackers replaced the agency's homepage with a slogan that said 'Reunification with Taiwan in 2021', it said.
An identical attack occurred a month ago when suspected Chinese hackers attacked the site of Taiwan President Chen Shui-bian's pro-independence Democratic Progressive Party.
Hong Kong's pro-Beijing Wen Wei Po daily last week quoted Chinese military sources as warning Taiwan must re-enter the Chinese fold or face military action within the next 20 years.
In response to Taiwan's recent "pro-independence provocation," Beijing gave what was believed to be the first ultimatum to reclaim sovereignty over the island, it said.
Unnamed military sources were quoted as saying former Chinese president and Central Military Commission chairman Jiang Zemin had recently discussed a timetable regarding using force to achieve Taiwan's reunification in a speech at a military conference in Beijing.
The fresh Internet attack came two days before Taiwanese air force is due to practice emergency landings on a freeway as part of measures against an attack by China, the defense ministry said.
Two French-made Mirage 2000-5s are set to land, refuel and load ammunition on the road in Tainan, southern Taiwan.
The exercise is designed to "review the air force's capability in using freeways for emergency landings and logistic support in case of war," defense ministry spokesman Huang Suey-sheng told reporters.
Since Chen's re-election in March, China has ratcheted up its rhetoric, reiterating its long-standing vow to take Taiwan by force should Chen move the island towards formal independence.
Beijing has considered Taiwan part of its territory awaiting reunification since the two sides split at the end of a civil war in 1949.