The protesters, demanding the resignation of the government of Prime Minister Yingluck Shinawatra, broke barricades and police lines in front of the ministry, China's Xinhua News Agency reported.
After a standoff that lasted hours, police at the ministry and the adjacent Budget Bureau retreated, allowing the protesters to occupy the premises, the report said.
Former Deputy Premier Suthep Thaugsuban, leading the protests, said his people planned to occupy other ministries beginning Tuesday in their effort to paralyze the Yingluck government.
On Sunday, about 100,000 demonstrators had turned up in Bangkok.
Thaugsuban urged civil servants to join the protests, CNN reported.
"We will separate into 13 groups to march to 13 locations to express our stance," he said. "Our protest will not stop until Thaksin's regime is wiped out."
Yingluck Shinawatra is the sister of former Premier Thaksin Shinawatra, a wealthy telecommunications businessman who was forced out in a 2006 coup. Critics accuse her of being a proxy for Thaksin, who has lived in exile since his ouster.
Yingluck came under fire for backing an amnesty bill that critics contend is designed to allow Thaksin to return to Thailand. Earlier this month, the Thai Senate rejected the bill but that has not helped stop the protests.
Yingluck Shinawatra has appealed for unity and reconciliation.
The Bangkok Nation said many of the protesters who had traveled to Bangkok from the provinces were camping out in large tents in the capital.