Police took the students and two activists from a civic group into custody, the Yonhap news agency said. They face police charges over what police said was a serious incident.
It is unclear if the US Ambassador to South Korea Harry Harris was on the premises during the incident but his Twitter feed indicates he spent the morning at an airspace and defence show at an aerospace exhibition at the Seoul airport.
The South Korean Foreign Ministry said "any harm to or attack on foreign diplomatic missions will not be justified." It called for security around US diplomatic property to be beefed up.
The protest comes amid talks between Seoul and Washington over how to share the cost of some 28,500 US troops that have been stationed in the country since the end of the Korean War. The negotiations are a part of the Special Measures Agreement (SMA) concluded earlier in February and demanding South Korea to raise its contribution to US Forces Korea to $923 million in 2019. US President Donald Trump has consistently urged South Korea to pay ''more money'' to ''defend itself from North Korea''.